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Journal articles on the topic 'Soliton solutions'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ma, Hongcai, Qiaoxin Cheng, and Aiping Deng. "N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation." Modern Physics Letters B 35, no. 10 (2021): 2150277. http://dx.doi.org/10.1142/s0217984921502778.

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[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the i

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2

Wang, Chunxia, Xiaojun Yin, and Liguo Chen. "Soliton molecules, bifurcation solitons and interaction solutions of a generalized (2 + 1)-dimensional korteweg-de vries system for the shallow-water waves." Physica Scripta 99, no. 10 (2024): 105272. http://dx.doi.org/10.1088/1402-4896/ad79a1.

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Abstract The central purpose of this paper is exploring the soliton molecules, bifurcation solitons and interaction solutions of the Korteweg–de Vries system based on the Hirota bilinear method. The studied system acts as an extension of the classic KdV system for the shallow-water waves, and is very useful to contribute in nonlinear wave phenomena. Firstly, the soliton molecules are obtained by adding resonance parameters in N-soliton. Then the interaction solutions between soliton/breather and soliton molecules are studied, as well as the interaction between two soliton molecules by using N-

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3

Sun, Ya, Bo Tian, Yu-Feng Wang, Yun-Po Wang, and Zhi-Ruo Huang. "Bright solitons and their interactions of the (3 + 1)-dimensional coupled nonlinear Schrödinger system for an optical fiber." Modern Physics Letters B 29, no. 35n36 (2015): 1550245. http://dx.doi.org/10.1142/s0217984915502450.

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Under investigation in this paper is the [Formula: see text]-dimensional coupled nonlinear Schrödinger system for an optical fiber with birefringence. With the Hirota method, bilinear forms of the system are derived via an auxiliary function, and the bright one- and two-soliton solutions are constructed. Based on those soliton solutions, soliton propagation and interaction are investigated analytically and graphically. Non-singular cases of the bright one-soliton solutions are presented, from which the single-peak and two-peak solitons can arise, respectively. Through the analysis on the brigh

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4

Hossain, Md Nur, M. Mamun Miah, Moataz Alosaimi, Faisal Alsharif, and Mohammad Kanan. "Exploring Novel Soliton Solutions to the Time-Fractional Coupled Drinfel’d–Sokolov–Wilson Equation in Industrial Engineering Using Two Efficient Techniques." Fractal and Fractional 8, no. 6 (2024): 352. http://dx.doi.org/10.3390/fractalfract8060352.

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The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, wh

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5

Yıldırım, Y., and A. Biswas. "Dispersive optical soliton perturbation with multiplicative white noise having parabolic law of self-phase modulation." Semiconductor Physics, Quantum Electronics and Optoelectronics 28, no. 01 (2025): 053–58. https://doi.org/10.15407/spqeo28.01.053.

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In this paper, we investigate dispersive optical solitons incorporating multiplicative white noise. Utilizing the F-expansion procedure, we derive various soliton solutions, including dark soliton solutions, singular soliton solutions, bright soliton solutions, straddled singular-singular soliton solutions, complexiton solutions, and straddled dark-bright soliton solutions. Moreover, we discuss the parametric restrictions necessary for the existence of these soliton solutions, providing a comprehensive analysis of the conditions under which these solutions are valid. Our findings contribute to

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6

Ma, Hongcai, Huaiyu Huang, and Aiping Deng. "Soliton molecules and some novel hybrid solutions for (3+1)-dimensional B-type Kadomtsev–Petviashvili equation." Modern Physics Letters B 35, no. 23 (2021): 2150388. http://dx.doi.org/10.1142/s0217984921503887.

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In recent years, soliton molecules have received reinvigorating scientific interests in physics and other fields. Soliton molecules have been successfully found in optical experiments. In this paper, we attribute the solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by employing the bilinear method. Based on the [Formula: see text]-soliton solutions, we establish the soliton molecules, asymmetric solitons and some novel hybrid solutions of this equation by means of the velocity resonance mechanism and the long wave limit method. Finally, we give dynamic graphs of

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7

Ahmed, Iftikhar, Aly R. Seadawy, and Dianchen Lu. "Mixed lump-solitons, periodic lump and breather soliton solutions for (2 + 1)-dimensional extended Kadomtsev–Petviashvili dynamical equation." International Journal of Modern Physics B 33, no. 05 (2019): 1950019. http://dx.doi.org/10.1142/s021797921950019x.

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In this study, based on the Hirota bilinear method, mixed lump-solitons, periodic lump and breather soliton solutions are derived for (2 + 1)-dimensional extended KP equation with the aid of symbolic computation. Furthermore, dynamics of these solutions are explained with 3d plots and 2d contour plots by taking special choices of the involved parameters. Through the mixed lump-soliton solutions, we observe two fusion phenomena, first from interaction of lump and single soliton and other from interaction of lump with two solitons. In both cases, lump moves gradually towards soliton and transfer

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8

Asjad, Muhammad Imran, Naeem Ullah, Hamood Ur Rehman, and Tuan Nguyen Gia. "Novel soliton solutions to the Atangana–Baleanu fractional system of equations for the ISALWs." Open Physics 19, no. 1 (2021): 770–79. http://dx.doi.org/10.1515/phys-2021-0085.

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Abstract This work deals the construction of novel soliton solutions to the Atangana–Baleanu (AB) fractional system of equations for the ion sound and Langmuir waves by using Sardar-subequation method (SSM). The outcomes are in the form of bright, singular, dark and combo soliton solutions. These solutions have wide applications in the arena of optoelectronics and wave propagation. The bright solitons will be a vast advantage in controlling the soliton disorder, dark solitons are also beneficial for soliton communication when a background wave exists and singular solitons only elaborate the sh

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9

Huang, Qian-Min, and Yi-Tian Gao. "Bilinear form, bilinear Bäcklund transformation and dynamic features of the soliton solutions for a variable-coefficient (3+1)-dimensional generalized shallow water wave equation." Modern Physics Letters B 31, no. 22 (2017): 1750126. http://dx.doi.org/10.1142/s0217984917501263.

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Under investigation in this letter is a variable-coefficient (3[Formula: see text]+[Formula: see text]1)-dimensional generalized shallow water wave equation. Bilinear form and Bäcklund transformation are obtained. One-, two- and three-soliton solutions are derived via the Hirota bilinear method. Interaction and propagation of the solitons are discussed graphically. Stability of the solitons is studied numerically. Soliton amplitude is determined by the spectral parameters. Soliton velocity is not only related to the spectral parameters, but also to the variable coefficients. Phase shifts are t

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10

Yang, Hongwei, Yong Zhang, Xiaoen Zhang, Xin Chen, and Zhenhua Xu. "The Rational Solutions and Quasi-Periodic Wave Solutions as well as Interactions ofN-Soliton Solutions for 3 + 1 Dimensional Jimbo-Miwa Equation." Advances in Mathematical Physics 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/7241625.

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The exact rational solutions, quasi-periodic wave solutions, andN-soliton solutions of 3 + 1 dimensional Jimbo-Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant

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11

Yang, Shuxin, Zhao Zhang, and Biao Li. "Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation." Advances in Mathematical Physics 2020 (January 7, 2020): 1–9. http://dx.doi.org/10.1155/2020/2670710.

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Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by N-soliton solutions and a new velocity resonance condition. Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics f

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12

Ahmed, Karim K., Niveen M. Badra, Hamdy M. Ahmed, and Wafaa B. Rabie. "Soliton Solutions and Other Solutions for Kundu–Eckhaus Equation with Quintic Nonlinearity and Raman Effect Using the Improved Modified Extended Tanh-Function Method." Mathematics 10, no. 22 (2022): 4203. http://dx.doi.org/10.3390/math10224203.

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Our paper studies the optical solitons for the Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying the improved modified extended tanh-function method, many soliton solutions can be obtained such as bright soliton solutions, dark soliton solutions, and the singular soliton solution. In addition, we can obtain various types of solutions, namely, singular periodic solutions, exponential solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some selected solutions are illustrated graphically to show t

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13

Rao, Jiguang, Kuppuswamy Porsezian, Jingsong He, and Thambithurai Kanna. "Dynamics of lumps and dark–dark solitons in the multi-component long-wave–short-wave resonance interaction system." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (2018): 20170627. http://dx.doi.org/10.1098/rspa.2017.0627.

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General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave–short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the f

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14

Mandal, Gurudas, Kaushik Roy, Anindita Paul, Asit Saha, and Prasanta Chatterjee. "Overtaking Collision and Phase Shifts of Dust Acoustic Multi-Solitons in a Four Component Dusty Plasma with Nonthermal Electrons." Zeitschrift für Naturforschung A 70, no. 9 (2015): 703–11. http://dx.doi.org/10.1515/zna-2015-0106.

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AbstractThe nonlinear propagation and interaction of dust acoustic multi-solitons in a four component dusty plasma consisting of negatively and positively charged cold dust fluids, non-thermal electrons, and ions were investigated. By employing reductive perturbation technique (RPT), we obtained Korteweged–de Vries (KdV) equation for our system. With the help of Hirota’s bilinear method, we derived two-soliton and three-soliton solutions of the KdV equation. Phase shifts of two solitons and three solitons after collision are discussed. It was observed that the parameters α, β, β1, μe, μi, and

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15

Wazwaz, Abdul-Majid. "A (2 + 1)-dimensional extension of the Benjamin-Ono equation." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 11 (2018): 2681–87. http://dx.doi.org/10.1108/hff-04-2018-0129.

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Purpose The purpose of this paper is concerned with developing a (2 + 1)-dimensional Benjamin–Ono equation. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for this equation. Design/methodology/approach The proposed model has been handled by using the Hirota’s method. Other techniques were used to obtain traveling wave solutions. Findings The examined extension of the Benjamin–Ono model features interesting results in propagation of waves and fluid flow. Research limitations/implications The paper presents a new efficient algorithm for constru

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16

Dai, Chao-Qing, Hai-Ping Zhu, and Chun-Long Zheng. "Tunnelling Effects of Solitons in Optical Fibers with Higher-Order Effects." Zeitschrift für Naturforschung A 67, no. 6-7 (2012): 338–46. http://dx.doi.org/10.5560/zna.2012-0033.

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We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly.We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons

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17

NA, LIANG, MIHALACHE DUMITRU, MINJIE MA, RAO JIGUANG, and LIU YIXIAN. "The multiple bright soliton pairs of the fully PT-symmetric nonlocal Davey-Stewartson I equation." Romanian Reports in Physics 76, no. 2 (2024): 106. http://dx.doi.org/10.59277/romrepphys.2024.76.106.

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This article investigates the dynamics of multiple bright soliton pair interactions in the fully PT -symmetric nonlocal Davey–Stewartson I equation. The bright soliton pair solutions are derived by employing the bilinear KP-hierarchy reduction method, and are expressed in terms of determinants. To study the interactions of the multiple soliton pairs, the long-time asymptotic analysis for these soliton solutions is performed by using the analysis of determinants, and the asymptotic expressions of the N individual soliton pair solutions are given as the sum of expressions for the 2N single solit

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18

Abdul Kayum, Md, Aly R. Seadawy, Ali M. Akbar, and Taghreed G. Sugati. "Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics." Open Physics 18, no. 1 (2020): 710–25. http://dx.doi.org/10.1515/phys-2020-0183.

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AbstractThe Sinh–Poisson equation and the RLC transmission line equation are important nonlinear model equations in the field of engineering and power transmission. The modified simple equation (MSE) procedure is a realistic, competent and efficient mathematical scheme to ascertain the analytic soliton solutions to nonlinear evolution equations (NLEEs). In the present article, the MSE approach is put forward and exploited to establish wave solutions to the previously referred NLEEs and accomplish analytical broad-ranging solutions associated with parameters. Whenever parameters are assigned de

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19

LIU, YUNKAI. "Dynamics of the multi-dark-soliton solutions on periodic backgrounds in the Maccari system." Romanian Reports in Physics 76, no. 2 (2025): 103. https://doi.org/10.59277/romrepphys.2025.77.103.

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This paper investigates the dynamics of multi-dark-soliton solutions on periodic backgrounds within the Maccari system. Utilizing the bilinear method, we construct the multiple-dark-soliton solutions on periodic background, represented in block determinant form. We discover that the dark solitons feature periodic waves on periodic backgrounds. The study explores the interaction behaviors of these dark solitons through asymptotic analysis, revealing significant effects of periodic backgrounds on the dark soliton dynamics. The results show that the periodic backgrounds influence the soliton ampl

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20

Rizvi, Syed Tahir Raza, Aly R. Seadawy, Ishrat Bibi, and Muhammad Younis. "Chirped and chirp-free optical solitons for Heisenberg ferromagnetic spin chains model." Modern Physics Letters B 35, no. 08 (2021): 2150139. http://dx.doi.org/10.1142/s0217984921501396.

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In this paper, we study (2+1)-dimensional non-linear spin dynamics of Heisenberg ferromagnetic spin chains equation (HFSCE) for various soliton solutions. We obtain two types of optical solitons i.e. chirp free and chirped solitons. We obtain bright and bright-like soliton, singular-like solitons, periodic and rational solutions, Weierstrass elliptic functions solutions and other solitary wave solutions for HFSCE with the aid of sub-ODE method. At the end, we present graphical representation of our solutions.

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21

Alhojilan, Yazid, Hamdy M. Ahmed, and Wafaa B. Rabie. "Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method." Symmetry 15, no. 1 (2023): 207. http://dx.doi.org/10.3390/sym15010207.

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Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons and other exact stochastic solutions through birefringent fibers for the Biswas–Arshed equation with multiplicative white noise using the modified extended mapping method. This model contains many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Stochastic bright soliton solutions, stochastic dark soliton solutions, stochastic combo bright–dark soliton solutions, stochastic combo singular-bright sol

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22

Jia, Xiao-Yue, Bo Tian, Zhong Du, Yan Sun, and Lei Liu. "Lump and rogue waves for the variable-coefficient Kadomtsev–Petviashvili equation in a fluid." Modern Physics Letters B 32, no. 10 (2018): 1850086. http://dx.doi.org/10.1142/s0217984918500860.

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Under investigation in this paper is the variable-coefficient Kadomtsev–Petviashvili equation, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Employing the bilinear form and symbolic computation, we obtain the lump, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions. Discussions indicate that the variable coefficients are related to both the lump soliton’s velocity and amplitude. Mixed lump-stripe soliton solutions display two different properties, fusion and fission. Mixed rogue wave-st

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23

Yin, Hui-Min, Bo Tian, Hui-Ling Zhen, Jun Chai, and Xiao-Yu Wu. "Bright optical solitons or light bullets for a (3 + 1)-dimensional generalized nonlinear Schrödinger equation with the distributed coefficients." Modern Physics Letters B 30, no. 25 (2016): 1650306. http://dx.doi.org/10.1142/s0217984916503061.

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Under investigation in this paper is a (3 + 1)-dimensional generalized nonlinear Schrödinger equation with the distributed coefficients for the spatiotemporal optical solitons or light bullets. Through the symbolic computation and Hirota method, one- and two-soliton solutions are derived. We also present the Bäcklund transformation, through which we derive the soliton solutions. When the gain/loss coefficient is the monotonically decreasing function for the propagation coordinate [Formula: see text], amplitude for the spatiotemporal optical soliton or light bullet decreases along [Formula: see

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24

XIAO, YAN, ZHIYONG XU, LU LI, ZHONGHAO LI, and GUOSHENG ZHOU. "SOLITON PROPAGATION IN NONUNIFORM OPTICAL FIBERS." Journal of Nonlinear Optical Physics & Materials 12, no. 03 (2003): 341–48. http://dx.doi.org/10.1142/s0218863503001444.

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In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two neighboring solitons.

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25

Le Coz, Stefan, Dong Li, and Tai-Peng Tsai. "Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 6 (2015): 1251–82. http://dx.doi.org/10.1017/s030821051500030x.

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We study infinite soliton trains solutions of nonlinear Schrödinger equations, i.e. solutions behaving as the sum of infinitely many solitary waves at large time. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of such a soliton train. We also give a new construction of multi-solitons (i.e. finite trains) and prove uniqueness in an exponentially small neighbourhood, and we consider the case of solutions composed of several solitons and kinks (i.e. solutions with a non-zero background at infinity).

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26

Yue, Yunfei, and Yong Chen. "Dynamics of localized waves in a (3+1)-dimensional nonlinear evolution equation." Modern Physics Letters B 33, no. 09 (2019): 1950101. http://dx.doi.org/10.1142/s021798491950101x.

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In this paper, a (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear evolution equation is studied via the Hirota method. Soliton, lump, breather and rogue wave, as four types of localized waves, are derived. The obtained N-soliton solutions are dark solitons with some constrained parameters. General breathers, line breathers, two-order breathers, interaction solutions between the dark soliton and general breather or line breather are constructed by choosing suitable parameters on the soliton solution. By the long wave limit method on the soliton solution, some new lump and rogue

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27

Biswas, Anjan, Jose Vega-Guzman, Yakup Yıldırım, Luminita Moraru, Catalina Iticescu, and Abdulah A. Alghamdi. "Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients." Mathematics 11, no. 9 (2023): 2012. http://dx.doi.org/10.3390/math11092012.

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In the current study, the concatenation model of birefringent fibers is explored for the first time, and we present optical soliton solutions to the model. The integration algorithm used to achieve this retrieval is the method of undetermined coefficients, which yields a wide range of soliton solutions. The parameter constraints arise naturally during the derivation of the soliton solutions, which are essential for such solitons to exist.

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Yan, Zhenya. "Abundant New Exact Solutions of the Coupled Potential KdV Equation and the Modified KdV-Type Equation." Zeitschrift für Naturforschung A 56, no. 12 (2001): 809–15. http://dx.doi.org/10.1515/zna-2001-1203.

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Abstract Exact solutions of nonlinear evolution equations (NLEEs)in soliton theory and their applications are studied. A powerful method is established to search for exact travelling wave solutions of NLEEs. We chose the coupled potential KdV equation and modified KdV-type equations presented by Foursov to illustrate the approach with the aid of Maple. As a result, eight families of exact solutions of the coupled potential KdV equation and nine families of exact solutions of the modified KdV-type equations are obtained, which contain new kink-like soliton solutions, kink shaped solitons, bell

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29

Xu, Tao, Bo Tian, and Feng-Hua Qi. "Bright N-Soliton Solutions to the Vector Hirota Equation from Nonlinear Optics with Symbolic Computation." Zeitschrift für Naturforschung A 67, no. 1-2 (2012): 39–49. http://dx.doi.org/10.5560/zna.2011-0055.

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Under investigation in this paper is the vector Hirota (VH) equation which governs the simultaneous propagation of multiple interacting femtosecond pulses in a certain type of coupled optical waveguides. By the Nth iterated Darboux transformation starting from the zero potential, the VH equation is found to admit the bright N-soliton solutions in terms of the multi-component Wronskian. Asymptotic formulae of the bright N-soliton solutions are derived for any given set of spectral parameters, which allows us to directly analyze the collision dynamics of VH solitons. Via symbolic computation, so

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30

GAI, XIAO-LING, YI-TIAN GAO, XIN YU, and ZHI-YUAN SUN. "SOLITON INTERACTIONS FOR THE GENERALIZED (3+1)-DIMENSIONAL BOUSSINESQ EQUATION." International Journal of Modern Physics B 26, no. 07 (2012): 1250062. http://dx.doi.org/10.1142/s0217979212500622.

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Generalized (3+1)-dimensional Boussinesq equation is investigated in this paper. Through the dependent variable transformation and symbolic computation, the one- and two-soliton solutions are obtained. With the one-soliton solution, the coefficient effects in the soliton propagation process are investigated. Through analyzing the two-soliton solution, two kinds of two-soliton interactions are presented: (i) Two solitons merge into a bigger one whose amplitude increases but does not exceed the sum of the two at the moment of the collision; (ii) Two solitons can pass through each other, and thei

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31

Ying, Jin-ping, and Sen-yue Lou. "Abundant Coherent Structures of the (2+1)-dimensional Broer-Kaup-Kupershmidt Equation." Zeitschrift für Naturforschung A 56, no. 9-10 (2001): 619–25. http://dx.doi.org/10.1515/zna-2001-0903.

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Abstract By using of the Bäcklund transformation, which is related to the standard truncated Painleve analysis, some types of significant exact soliton solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation are obtained. A special type of soliton solutions may be described by means of the variable coefficient heat conduction equation. Due to the entrance of infinitely many arbitrary functions in the general expressions of the soliton solution the solitons of the (2+1)- dimensional Broer-Kaup equation possess very abundant structures. By fixing the arbitrary functions appropriately,

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32

Sun, Hong-Qian, and Zuo-Nong Zhu. "Darboux Transformation and Soliton Solution of the Nonlocal Generalized Sasa–Satsuma Equation." Mathematics 11, no. 4 (2023): 865. http://dx.doi.org/10.3390/math11040865.

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This paper aims to seek soliton solutions for the nonlocal generalized Sasa–Satsuma (gSS) equation by constructing the Darboux transformation (DT). We obtain soliton solutions for the nonlocal gSS equation, including double-periodic wave, breather-like, KM-breather solution, dark-soliton, W-shaped soliton, M-shaped soliton, W-shaped periodic wave, M-shaped periodic wave, double-peak dark-breather, double-peak bright-breather, and M-shaped double-peak breather solutions. Furthermore, interaction of these solitons, as well as their dynamical properties and asymptotic analysis, are analyzed. It w

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33

Houwe, Alphonse, Mibaile Justin, Jérôme Dikwa, Gambo Betchewe, Serge Y. Doka, and Kofane Timoleon Crepin. "Exact soliton solutions for the perturbed nonlinear Schrödingers equation in left-handed metamaterials." Asian-European Journal of Mathematics 13, no. 02 (2018): 2050036. http://dx.doi.org/10.1142/s1793557120500369.

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This paper studies an exact soliton solutions for the perturbed nonlinear Schrödingers equation which describes the dynamics of ultrashort optical solitons in nonlinear left-handed metamaterials. To befall soliton solutions, the function transformation method is apply. Dark, bright and exact travelling wave solutions like Jacobi’s elliptic function solutions are reported.

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Al-Ghafri, K. S. "Different Physical Structures of Solutions for a Generalized Resonant Dispersive Nonlinear Schrödinger Equation with Power Law Nonlinearity." Journal of Applied Mathematics 2019 (February 3, 2019): 1–8. http://dx.doi.org/10.1155/2019/6143102.

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In this work, we investigate various types of solutions for the generalised resonant dispersive nonlinear Schrödinger equation (GRD-NLSE) with power law nonlinearity. Based on simple mathematical techniques, the complicated form of the GRD-NLSE is reduced to an ordinary differential equation (ODE) which has a variety of solutions. The analytic solution of the resulting ODE gives rise to bright soliton, singular soliton, peaked soliton, compacton solutions, solitary pattern solutions, rational solution, Weierstrass elliptic periodic type solutions, and some other types of solutions. Constraint

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Li, Wen-Tao, Jia-Heng Li, and Biao Li. "Soliton molecules, asymmetric solitons and some new types of hybrid solutions in (2+1)-dimensional Sawada–Kotera model." Modern Physics Letters B 34, no. 13 (2020): 2050141. http://dx.doi.org/10.1142/s0217984920501419.

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Soliton molecules can be formed in both theoretical and experimental situations. In this paper, a new velocity resonance is introduced, which can form soliton molecules for the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera equation. By selecting some suitable parameters for soliton molecules, the asymmetric solitons of the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera equation can be obtained. And, the interactions among multiple soliton molecules are elastic. Furthermore, some new types of hybrid solutions consisting of soliton molecules, lump w

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Liu, Xi-zhong, Zhi-Mei Lou, Xian-Min Qian, and Lamine Thiam. "A Study on Lump and Interaction Solutions to a (3 + 1)-Dimensional Soliton Equation." Complexity 2019 (October 16, 2019): 1–12. http://dx.doi.org/10.1155/2019/9857527.

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Based on bilinear formulation of a (3 + 1)-dimensional soliton equation, lump solution and related interaction solutions are investigated. The lump solutions of the soliton equation are classified into three cases with nonsingularity conditions being given. The interaction solutions between lump and a stripe soliton are obtained in eight cases, which have interesting fusing and fission behaviors with changing time. The interaction solutions of the soliton equation between a lump and a resonant pair of stripe solitons are also given, and we find that the lump just exist for a finite period duri

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Al-Ghafri, Khalil Salim. "Soliton structures in optical fiber communications with Kundu–Mukherjee–Naskar model." Open Physics 19, no. 1 (2021): 679–82. http://dx.doi.org/10.1515/phys-2021-0074.

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Abstract In the present work, we investigate soliton structures in optical fiber communications. The medium is described by the Kundu–Mukherjee–Naskar model. With the aid of the ansatz approach, the exact solutions are constructed. Consequently, distinct wave structures including W-shaped, bright and dark solitons are derived. These new soliton solutions are retrieved under certain parametric conditions. Besides, it is found that the bright soliton has two different types in a particular limit. Optical solitons are displayed graphically to shed light on their behaviors.

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NAVICKAS, ZENONAS, TADAS TELKSNYS, INGA TIMOFEJEVA, MINVYDAS RAGULSKIS, and ROMAS MARCINKEVICIUS. "AN ANALYTICAL SCHEME FOR THE ANALYSIS OF MULTI-HUMP SOLITONS." Advances in Complex Systems 22, no. 01 (2019): 1850027. http://dx.doi.org/10.1142/s0219525918500273.

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An analytical framework for the analysis of multi-hump solitons is proposed in this paper. Multi-hump solitons are defined by imposing special symmetry conditions on the classical soliton expression. Such soliton solutions have a wide range of potential applications in the field of optical communications. The proposed algebras of soliton solutions enable a new look at the propagation dynamics of complex nonlinear wave phenomena. The efficiency of the presented analytical scheme is demonstrated using a system of Riccati differential equations with diffusive and multiplicative coupling.

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YANG, QIN, and JIE-FANG ZHANG. "OPTICAL QUASI-SOLITON SOLUTIONS FOR THE CUBIC-QUINTIC NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS." International Journal of Modern Physics B 19, no. 31 (2005): 4629–36. http://dx.doi.org/10.1142/s0217979205033005.

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Optical quasi-soliton solutions for the cubic-quintic nonlinear Schrödinger equation (CQNLSE) with variable coefficients are considered. Based on the extended tanh-function method, we not only successfully obtained bright and dark quasi-soliton solutions, but also obtained the kink quasi-soliton solutions under certain parametric conditions. We conclude that the quasi-solitons induced by the combined effects of the group velocity dispersion (GVD) distribution, the nonlinearity distribution, higher-order nonlinearity distribution, and the amplification or absorption coefficient are quite differ

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MAT ZIN, S., W. N. M. ARIFFIN, and S. A. HASHIM ALI. "SIMULATION OF KORTEWEG DE VRIES EQUATION." International Journal of Modern Physics: Conference Series 09 (January 2012): 574–80. http://dx.doi.org/10.1142/s2010194512005685.

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Korteweg de Vries (KdV) equation has been used as a mathematical model of shallow water waves. In this paper, we present one-, two-, and three-soliton solution of KdV equation. By definition, soliton is a nonlinear wave that maintains its properties (shape and velocity) upon interaction with each other. In order to investigate the behavior of soliton solutions of KdV equation and the interaction process of the two- and three-solitons, computer programs have been successfully simulated. Results from these simulations confirm that the solutions of KdV equation obtained are the soliton solutions.

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ZHEN, HUI-LING, BO TIAN, PAN WANG, RONG-XIANG LIU, and HUI ZHONG. "SOLITON INTERACTION OF THE ZAKHAROV–KUZNETSOV EQUATIONS IN PLASMA DYNAMICS." International Journal of Modern Physics B 27, no. 09 (2013): 1350029. http://dx.doi.org/10.1142/s021797921350029x.

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In this paper we investigate the constant- and variable-coefficient Zakharov–Kuznetsov (ZK) equations respectively for the electrostatic solitons and two-dimensional ion-acoustic waves obliquely propagating in the inhomogeneous magnetized two-ion-temperature dusty plasmas. By virtue of the symbolic computation and Hirota method, new bilinear forms and N-soliton solutions are both derived. Asymptotic analysis on two-soliton solutions indicates that the soliton interaction is elastic. Propagation characteristics and interaction behavior of the solitons are discussed via graphical analysis. Effec

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Khalifa, Abeer S., Hamdy M. Ahmed, Niveen M. Badra, Wafaa B. Rabie, Farah M. Al-Askar, and Wael W. Mohammed. "New soliton wave structure and modulation instability analysis for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities." AIMS Mathematics 9, no. 9 (2024): 26166–81. http://dx.doi.org/10.3934/math.20241278.

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<p>We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. Th

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Alurrfi, Khaled A., Ragab M. Almasroub, Omar A. Aleyan, and Marwa A. Saeid. "Exact Solutions in Birefringent Fibers for Stochastic N-LSE with Kerr-Law Nonlinearity and Multiplicative White Noise Effects." International Science and Technology Journal 36, no. 1 (2025): 1–25. https://doi.org/10.62341/krom2154.

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This article explores the exact wave solutions of the coupled one-dimensional stochastic non-linear Schrödinger equation with Kerr-law nonlinearity, incorporating multiplicative white noise in the Itô interpretation. The generalized projective Riccati equations (GPREs) scheme is employed to obtain the obtained solutions. The study presents a range of soliton solutions, including dark, bright, singular solitons, in addition to solutions for rational and periodic functions. Finally, the MATLAB software was used to explain the numerical simulation of some soliton solutions. Keywords: Generalized

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Hamali, Waleed, Hamad Zogan, and Abdulhadi A. Altherwi. "Dark and bright hump solitons in the realm of the quintic Benney-Lin equation governing a liquid film." AIMS Mathematics 9, no. 10 (2024): 29167–96. http://dx.doi.org/10.3934/math.20241414.

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<p>This study explored and examined soliton solutions for the Quintic Benney-Lin equation (QBLE), which describes the dynamic of liquid films, using the Riccati modified extended simple equation method (RMESEM). The proposed approach, which is designed for nonlinear partial differential equations (NPDEs), effectively generates a large number of soliton solutions for the given QBLE, which basically captures the fundamental dynamics of the system. The rational, hyperbolic, rational-hyperbolic, trigonometric, and exponential forms of the scientifically specified soliton solutions are the ma

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Li, Wenjing, Yi Zhang, and Xiaolin Yang. "Riemann-Hilbert approach and multiple high-order pole solutions for the AB system." Communications in Theoretical Physics, August 13, 2024. http://dx.doi.org/10.1088/1572-9494/ad6e63.

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Abstract This article's purpose is to investigate multiple high-order pole solutions for the AB system by Riemann-Hilbert (RH) approach. We establish RH problem through using spectral analysis to the Lax pair. Then the RH problem can be resolved and the soliton solution's formula can be given by using Laurent expansion method. Finally we get special soliton solutions, including dark solitons, W-type dark solitons and multiple high-pole solutions. In addition, the W-type dark soliton solutions will occur when the spectral parameters are purely imaginary.

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Li, Nan, and Ming Wang. "Dark soliton, rational solution and breather for the Hirota-Satsuma equation." Physica Scripta, July 8, 2025. https://doi.org/10.1088/1402-4896/aded4a.

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Abstract This paper investigates the localized waves of the Hirota-Satsuma equation under the nonzero continuous wave background. The Hirota-Satsuma equation relates to the Boussinesq equation through the Miura transformation. The bilinear form of Hirota-Satsuma equation is given through four identities under the bi-logarithmic transformation. N-soliton solutions and the first two soliton solutions are presented explicitly. The one-soliton solution admits dark or antidark soliton depending on the parametric condition, which decides the soliton type. The interactions between antidark and dark s

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Li, Wenjing, Yi Zhang, and Xiaolin Yang. "Riemann-Hilbert approach and multi-soliton solutions of nonlocal Newell-type long wave-short wave equation." Physica Scripta, June 7, 2024. http://dx.doi.org/10.1088/1402-4896/ad5591.

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Abstract This article's purpose is to investigate the inverse scattering transform of the nonlocal long wave-short wave (LW-SW) equation and its multi-soliton solutions via Riemann-Hilbert (RH) approach. By using spectral analysis to the Lax pair of LW-SW equation, the RH problem can be constructed. However, we consider spectral analysis from the time part rather than the usual space part, since it is hard to obtain the analyticity of the space part. Then the RH problem can be solved and the formula of the soliton solutions can be given. We provide several special soliton solutions including Y

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Wang, Lu, Li Li, and Fajun Yu. "Some anomalous exact solutions for the four-component coupled nonlinear Schrödinger equations on complex wave backgrounds." Scientific Reports 12, no. 1 (2022). http://dx.doi.org/10.1038/s41598-022-20253-0.

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AbstractThe coupled nonlinear Schrödinger (CNLS) equations are the important models for the study of the multicomponent Bose-Einstein condensates (BECs). In this paper, we study the four-components CNLS equations via Darboux transformation and obtain the N-soliton solutions with zero seed and non-zero seed solutions($$q_i=0$$ q i = 0 or $$q_i=e^{-2it})$$ q i = e - 2 i t ) . The 1-soliton solution and 2-soliton solution are calculated on complex wave backgrounds, the dark-bright-bright-bright soliton solutions and dark-dark-bright-bright soliton solutions are constructed. We can obtain a new cl

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Shehzad, Farrukh, Aly R. Seadawy, Sarfaraz Ahmed, and Syed T. R. Rizvi. "Mathematical modeling and component generalization of (2+1)-dimensional Schwarz–Kortweg–de Vries model in shallow water waves." Modern Physics Letters B, March 5, 2024. http://dx.doi.org/10.1142/s0217984924502555.

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This work employs the sub-ODE method to compute new soliton solutions for the component generalization of [Formula: see text]-dimensional Schwarz–Kortweg–de Vries (SKdV) equation in shallow water waves. The rational soliton solutions (RSS), Jacobian elliptic function (JEF), periodic solutions (PS), hyperbolic function solutions (HFS), positive solitons, dark soliton solutions (DSS) and bright soliton solutions (BSS) are constructed with this technique. Solitons-like solutions, HFS and trigonometric-function solutions (TFS) are also found as the JEF’s parameter m approaches values of 1 and 0, r

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50

Wang, Ming, Guoliang He, Tao Xu, and Yitong Han. "Breather, soliton, multiple-pole, and interaction solutions to the Hirota–Satsuma equation." Physics of Fluids 36, no. 11 (2024). http://dx.doi.org/10.1063/5.0237457.

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In this paper, we investigate serval types of localized waves of the Hirota–Satsuma equation by using the Hirota method. By means of two identities, the bilinear form of the Hirota–Satsuma equation is proposed. Then, the one-, two-, and three-soliton solutions are given explicitly and analyzed. The one-soliton solution could present the type of soliton or antisoliton, which depends on the sign of the wave number. The soliton–soliton, soliton–antisoliton, and antisoliton–antisoliton interactions are analyzed through graphics in the two-soliton solution case. The interactions among three soliton

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