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Journal articles on the topic 'Soliton order'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Alkinzawi, Sheimaa A. Fengen, and Hassan A. Yasser. "Study of Soliton Interaction in Optical Fibers with Third Order Dispersion and Higher Order Nonlinear Effects." University of Thi-Qar Journal of Science 10, no. 2 (2023): 216–23. http://dx.doi.org/10.32792/utq/utjsci/v10i2.1114.

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In this paper, we present a numerical approach to solve the GNLSE and analyze soliton interaction phenomena using COMSOL environment. By leveraging the capabilities of COMSOL's PDE module, we can accurately capture the dynamics of solitons and investigate their interactions. We analyze the impact of different parameters such as soliton power, initial separation distance, and dispersion characteristics on the soliton dynamics. Furthermore, we examine the role of higher-order dispersion terms in shaping the soliton interactions. Our findings demonstrate the effectiveness of the proposed numerica

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2

Wang, Yutian, Fanglin Chen, Songnian Fu, et al. "Nonlinear Fourier transform assisted high-order soliton characterization." New Journal of Physics 24, no. 3 (2022): 033039. http://dx.doi.org/10.1088/1367-2630/ac5a86.

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Abstract Nonlinear Fourier transform (NFT), based on the nonlinear Schrödinger equation, is implemented for the description of soliton propagation, and in particular focused on propagation of high-order solitons. In nonlinear frequency domain, a high-order soliton has multiple eigenvalues depending on the soliton amplitude and pulse-width. During the propagation along the standard single mode fiber (SSMF), their eigenvalues remain constant, while the corresponding discrete spectrum rotates along with the SSMF transmission. Consequently, we can distinguish the soliton order based on its eigenva

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3

Khelil, Khadidja, Azzeddine Dekhane, Aissa Benselhoub, and Stefano Bellucci. "Higher order dispersions effect on high-order soliton interactions." Technology audit and production reserves 2, no. 1(70) (2023): 24–29. http://dx.doi.org/10.15587/2706-5448.2023.277346.

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The object of the research is deleting the interaction of the higher order soliton interaction by introducing the third and fourth order dispersions inside an optical fiber. The results are obtained by the simulation of the nonlinear Schrödinger equation, which models the propagation of solitons in the optical fiber using the method of Fast Fourier Transform. The interaction of two higher order solitons due to the attraction of their electric field can lead to losing the solitons' properties. Hence, this can prevent the use of solitons in high-bit-rate optical fiber communication systems becau

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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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5

PENG, GANG-DING, and ADRIAN ANKIEWICZ. "FUNDAMENTAL AND SECOND-ORDER SOLITION TRANSMISSION IN NONLINEAR DIRECTIONAL FIBER COUPLERS." Journal of Nonlinear Optical Physics & Materials 01, no. 01 (1992): 135–50. http://dx.doi.org/10.1142/s021819919200008x.

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Transmission characteristics of first-order and second-order solitons propagating through a nonlinear optical fiber coupler are investigated by analysing the coupled nonlinear Schrödinger equations (NLSEs). We show that it is most advantageous to use fundamental solitions to make an ideal optical switch which can be used in multiplexing and/or demultiplexing soliton signals from different sources, and that such a switch can have a high switching efficiency and intact soliton output. Also, we have analyzed the relation between critical power of a soliton switch and that of a cw switch, and have

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6

Pei, Zhi-Jie, and Hai-Qiang Zhang. "Higher-order rational soliton solutions for the fifth-order modified KdV and KdV equations." International Journal of Modern Physics B 35, no. 03 (2021): 2150036. http://dx.doi.org/10.1142/s0217979221500363.

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In this paper, we construct the generalized perturbation ([Formula: see text], [Formula: see text])-fold Darboux transformation of the fifth-order modified Korteweg-de Vries (KdV) equation by the Taylor expansion. We use this transformation to derive the higher-order rational soliton solutions of the fifth-order modified KdV equation. We find that these higher-order rational solitons admit abundant interaction structures. We graphically present the dynamics behaviors from the first- to fourth-order rational solitons. Furthermore, by the Miura transformation, we obtain the complex rational soli

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7

Jasim AL-Taie, Mohammed Salim, and Wisam Roiss Matrood. "Optimize Nonlinear Effects on Fundamental and High-order Soliton in Photonic Crystal Fiber." Malaysian Journal of Fundamental and Applied Sciences 20, no. 2 (2024): 320–27. http://dx.doi.org/10.11113/mjfas.v20n2.3299.

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Nonlinear effects in optical fibers are mainly caused by two sources: inelastic scattering behaviour or the intensity sensitivity of the medium's refractive index. The propagation process in photonic crystal fibers is more complex than the propagation process of first-order solitons, second-order solitons, and third-order solitons. This article discusses the effects of propagation on first-, second- and third-order solitons. A popular approach to supercontinuum generation through soliton fission is the higher-order soliton technique for spectral generation.

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8

Zhu, Wei, Hai-Fang Song, Wan-Li Wang, and Bo Ren. "Soliton Molecules, Multi-Lumps and Hybrid Solutions in Generalized (2 + 1)-Dimensional Date–Jimbo–Kashiwara–Miwa Equation in Fluid Mechanics." Symmetry 17, no. 4 (2025): 538. https://doi.org/10.3390/sym17040538.

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The generalized (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (gDJKM) equation, which can be used to describe some phenomena in fluid mechanics, is investigated based on the multi-soliton solution. Soliton molecules of the gDJKM equation are given by the velocity resonance mechanism. A soliton molecule containing three solitons is portrayed at different times. The invariance of the relative positions of three solitons confirms that they form a soliton molecule. Multi-order lumps are obtained by applying the long-wave limit method in the multi-soliton. By analyzing the dynamics of one-order and

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9

Mao, Dong, Zhiwen He, Qun Gao, et al. "Birefringence-Managed Normal-Dispersion Fiber Laser Delivering Energy-Tunable Chirp-Free Solitons." Ultrafast Science 2022 (July 30, 2022): 1–12. http://dx.doi.org/10.34133/2022/9760631.

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Chirp-free solitons have been mainly achieved with anomalous-dispersion fiber lasers by the balance of dispersive and nonlinear effects, and the single-pulse energy is constrained within a relatively small range. Here, we report a class of chirp-free pulse in normal-dispersion erbium-doped fiber lasers, termed birefringence-managed soliton, in which the birefringence-related phase-matching effect dominates the soliton evolution. Controllable harmonic mode locking from 5 order to 85 order is obtained at the same pump level of ~10 mW with soliton energy fully tunable beyond ten times, which indi

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10

Jia, Hui-Xian, and Dong-Ming Shan. "Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation." Zeitschrift für Naturforschung A 72, no. 11 (2017): 1071–75. http://dx.doi.org/10.1515/zna-2017-0227.

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AbstractIn this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do

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11

Seadawy, Aly R., Naila Nasreen, and Dianchen Lu. "Complex model ultra-short pulses in optical fibers via generalized third-order nonlinear Schrödinger dynamical equation." International Journal of Modern Physics B 34, no. 17 (2020): 2050143. http://dx.doi.org/10.1142/s021797922050143x.

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In this paper, several types of solitons such as dark soliton, bright soliton, periodic soliton, kink soliton and solitary waves in three-dimensional and two-dimensional contour plot have been derived for the generalized third-order nonlinear Schrödinger dynamical equations (NLSEs). The generalized third-order NLSE is a significant model ultra-short pulses in optical fibers. The computational work and outcomes achieved show the influence and efficiency of current method. Furthermore, we can solve many other higher-order NLSEs with the help of simple and effective technique.

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12

Ullah, Naeem, Muhammad Imran Asjad, Jan Awrejcewicz, Taseer Muhammad, and Dumitru Baleanu. "On soliton solutions of fractional-order nonlinear model appears in physical sciences." AIMS Mathematics 7, no. 5 (2022): 7421–40. http://dx.doi.org/10.3934/math.2022415.

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<abstract><p>In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)-dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardar-subequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. Fr

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13

Wang, Pan. "Bilinear form and soliton solutions for the fifth-order Kaup–Kupershmidt equation." Modern Physics Letters B 31, no. 06 (2017): 1750057. http://dx.doi.org/10.1142/s0217984917500579.

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In this paper, multi-soliton solutions of the fifth-order Kaup–Kupershmidt (KK) equation have been derived via the auxiliary function in conjunction with the bilinear method. These solutions have not been previously obtained. Propagation and interactions of three solitons have been presented analytically. The direction of the soliton is related to the signs of the parameters [Formula: see text]. The distances of the solitons are related to the values of the parameters [Formula: see text].

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14

Ho, Pak Tung. "Soliton to the higher-order curvature flow on surfaces." Publicationes Mathematicae Debrecen 107, no. 1-2 (2025): 33–50. https://doi.org/10.5486/pmd.2025.9876.

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Schwetlick introduced in [34] a sixth- and an eighth-order conformal flow on surfaces. In this paper, we consider solitons to these flows. We prove that any compact soliton must be trivial. We also prove some rigidity results for noncompact solitons.

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15

Tian, He-Yuan, Bo Tian, Yan Sun, and Su-Su Chen. "Generalized Darboux transformation and asymptotic analysis on the degenerate dark-bright solitons for a coupled nonlinear Schrödinger system." Physica Scripta 96, no. 12 (2021): 125263. http://dx.doi.org/10.1088/1402-4896/ac38d7.

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Abstract In this paper, our work is based on a coupled nonlinear Schrödinger system in a two-mode nonlinear fiber. A (N,m)-generalized Darboux transformation is constructed to derive the Nth-order solutions, where the positive integers N and m denote the numbers of iterative times and of distinct spectral parameters, respectively. Based on the Nth-order solutions and the given steps to perform the asymptotic analysis, it is found that a degenerate dark-bright soliton is the nonlinear superposition of several asymptotic dark-bright solitons possessing the same profile. For those asymptotic dark

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16

LEE, CHUN-TE, JINN-LIANG LIU, CHUN-CHE LEE, and YAW-HONG KANG. "THE SECOND-ORDER KdV EQUATION AND ITS SOLITON-LIKE SOLUTION." Modern Physics Letters B 23, no. 14 (2009): 1771–80. http://dx.doi.org/10.1142/s0217984909019934.

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This paper presents both the theoretical and numerical explanations for the existence of a two-soliton solution for a second-order Korteweg-de Vries (KdV) equation. Our results show that there exists "quasi-soliton" solutions for the equation in which solitary waves almost retain their identities in a suitable physical regime after they interact, and bear a close resemblance to the pure KdV solitons.

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17

Ghosh, B., and K. P. Das. "Effects of higher-order nonlinearity and finite geometry on the propagation of KdV solitons." Journal of Plasma Physics 40, no. 3 (1988): 545–52. http://dx.doi.org/10.1017/s0022377800013507.

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Using reductive perturbation theory and a planar waveguide geometry, the effects of higher-order nonlinearity and finite boundaries on the propagation of electron plasma and ion-acoustic KdV solitons are investigated by taking into account finite electron and ion temperatures. For an electron plasma wave, the higher-order nonlinearity is found to increase the amplitude of the soliton and slightly decrease the width of the soliton compared with that predicted by the first-order theory. For an ion-acoustic wave the higher-order-nonlinearity and finite-boundary effects give rise to a W-shaped sol

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18

Zhong, Hui, and Bo Tian. "Stochastic Soliton Solutions of the High-Order Nonlinear Schrödinger Equation in the Optical Fiber with Stochastic Dispersion and Nonlinearity." Zeitschrift für Naturforschung A 69, no. 1-2 (2014): 21–33. http://dx.doi.org/10.5560/zna.2013-0071.

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In this paper, the high-order nonlinear Schrödinger (HNLS) equation driven by the Gaussian white noise, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is studied. With the white noise functional approach and symbolic computation, stochastic one- and two-soliton solutions for the stochastic HNLS equation are obtained. For the stochastic one soliton, the energy and shape keep unchanged along the soliton propagation, but the velocity and phase shift change randomly because of the effects of Gaussian white noise. Ranges of the changes increas

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19

BISWAS, ANJAN, DANIELA MILOVIC, and DEJAN MILIC. "SOLITONS IN ALPHA-HELIX PROTEINS BY HE'S VARIATIONAL PRINCIPLE." International Journal of Biomathematics 04, no. 04 (2011): 423–29. http://dx.doi.org/10.1142/s1793524511001325.

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This paper studies the dynamics of solitons due to solitons in α-helix proteins. The analysis is going to be carried out by the aid of He's semi-inverse variational principle. The constraint relation between the soliton parameters will also be determined in order for the soliton to exist.

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20

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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21

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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22

Ali, Rustam, and Prasanta Chatterjee. "Three-Soliton Interaction and Soliton Turbulence in Superthermal Dusty Plasmas." Zeitschrift für Naturforschung A 74, no. 9 (2019): 757–66. http://dx.doi.org/10.1515/zna-2018-0452.

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AbstractPropagation and interaction of three solitons are studied within the framework of the Korteweg-de Vries (KdV) equation. The KdV equation is derived from an unmagnetised, collision-less dusty plasma containing cold inertial ions, stationary dusts with negative charge, and non-inertial kappa-distributed electrons, using the reductive perturbation technique (RPT). Adopting Hirota’s bilinear method, the three-soliton solution of the KdV equation is obtained and, as an elementary act of soliton turbulence, a study on the soliton interaction is presented. The concavity of the resulting pulse

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23

LI, BIAO. "EXACT SOLITON SOLUTIONS FOR THE HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION." International Journal of Modern Physics C 16, no. 08 (2005): 1225–37. http://dx.doi.org/10.1142/s0129183105007832.

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Based on the complex envelope ansatz method, the projective Riccati equation method and q-deformed hyperbolic functions, a method is developed for constructing a series of exact analytical solutions for higher-order nonlinear Schrödinger (HNLS) equation, which describes propagation of femtosecond light pulse in optical fiber under certain parametric conditions. With the help of symbolic computation, six families of new solitary wave solutions are obtained. The solitary wave solutions obtained by Li et al.18 are special cases of our solutions. The novel soliton solutions can describe W-shaped,

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24

Zuo, Da-Wei, Yi-Tian Gao, Yu-Hao Sun, Yu-Jie Feng, and Long Xue. "Multi-Soliton and Rogue-Wave Solutions of the Higher-Order Hirota System for an Erbium-Doped Nonlinear Fiber." Zeitschrift für Naturforschung A 69, no. 10-11 (2014): 521–31. http://dx.doi.org/10.5560/zna.2014-0045.

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AbstractThe nonlinear Schrödinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration.Wave propagation and interaction are analyzed: (i) Bell-sha

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25

Uddin, M. Hafiz, Mohammad Asif Arefin, M. Ali Akbar, and Mustafa Inc. "New Explicit Solutions to the Fractional-Order Burgers’ Equation." Mathematical Problems in Engineering 2021 (June 11, 2021): 1–11. http://dx.doi.org/10.1155/2021/6698028.

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The closed-form wave solutions to the time-fractional Burgers’ equation have been investigated by the use of the two variables G ′ / G , 1 / G -expansion, the extended tanh function, and the exp-function methods translating the nonlinear fractional differential equations (NLFDEs) into ordinary differential equations. In this article, we ascertain the solutions in terms of tanh , sech , sinh , rational function, hyperbolic rational function, exponential function, and their integration with parameters. Advanced and standard solutions can be found by setting definite values of the parameters in t

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26

PANG, XIAO-FENG, HUAI-WU ZHANG, JIA-FENG YU, and YU-HUI LUO. "INFLUENCES OF VARIATIONS OF CHARACTERISTIC PARAMETERS OF PROTEIN MOLECULES ON STATES OF SOLITON TRANSPORTED BIO-ENERGY." International Journal of Modern Physics B 20, no. 21 (2006): 3027–48. http://dx.doi.org/10.1142/s0217979206034960.

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We simulate numerically the dynamic properties of new soliton with quasi-coherent two quanta in the improved model by fourth-order Runge–Kutta way. We observed that the window of formation of new soliton is shifted toward smaller values of coupling constants when compared with the Davydov's soliton with one quantum and Förner's soliton with two quantum model. The new soliton formation starts at (χ1+χ2)=20 PN , and pinning starts from (χ1+χ2)=86 PN . The pinned solitons are also observed if both quanta are on the same end of the chain in the initial state. The behaviors of new soliton are varie

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27

Guo, Fan, and Ji Lin. "Lump, mixed lump-soliton, and periodic lump solutions of a (2+1)-dimensional extended higher-order Broer–Kaup System." Modern Physics Letters B 34, no. 33 (2020): 2050384. http://dx.doi.org/10.1142/s0217984920503844.

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In this paper, a (2+1)-dimensional extended higher-order Broer–Kaup system is introduced and its bilinear form is presented from the truncated Painlevé expansion. By taking the auxiliary function as the ansatzs including quadratic, exponential, and trigonometric functions, lump, mixed lump-soliton, and periodic lump solutions are derived. The mixed lump-soliton solutions are classified into two cases: the first one describes the non-elastic collision between one lump and one line soliton, which exhibits fission and fusion phenomena. The second one depicts the interaction consisting of one lump

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Sun, Yan, Bo Tian, Xiao-Yu Wu, Lei Liu, and Yu-Qiang Yuan. "Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber." Modern Physics Letters B 31, no. 12 (2017): 1750065. http://dx.doi.org/10.1142/s0217984917500658.

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Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with [Formula: see text], [Formula: see text] and [Formula: see text], which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficien

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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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Kangmafo Miendjim, Willy André, Caouis Kammegne, Thomas Tamo Tatietse, and Jimmi Hervé Talla Mbé. "Effect of the Dispersion Orders on the Widths of the Coexistence Domain and Combs Spectra of Bright and Dark Solitons in Microresonators." International Journal of Optics 2023 (December 8, 2023): 1–8. http://dx.doi.org/10.1155/2023/5537645.

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Using the Lugiato–Lefever model, we base on the hysteresis approach to analyze the coexistence domain of bright and dark solitons in the zero, normal, and anomalous dispersion regimes. Our results also highlight that the fourth-order dispersion term affects the width of the frequency combs of both dark and bright solitons. It also allows the appearance of dispersive waves on the soliton spectra that disappear for high values of the fourth-order dispersion followed by the soliton destabilization into harmonic oscillations and oscillation packages.

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Zhang, Guoqiang, and Zhenya Yan. "The n -component nonlinear Schrödinger equations: dark–bright mixed N - and high-order solitons and breathers, and dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2215 (2018): 20170688. http://dx.doi.org/10.1098/rspa.2017.0688.

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The general n -component nonlinear Schrödinger equations are systematically investigated with the aid of the Darboux transformation method and its extension. Firstly, we explore the condition of the existence for dark–bright mixed soliton solutions and derive an explicit formula of dark–bright mixed multi-soliton solutions in terms of the determinant. Secondly, we present the formula of dark–bright mixed high-order semi-rational solitons, and predict their general N th-order wave structures. Thirdly, we investigate the wing-shaped structures of breather. Finally, we perform the numerical simul

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Shwetanshumala, S. "Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions." Zeitschrift für Naturforschung A 71, no. 2 (2016): 175–84. http://dx.doi.org/10.1515/zna-2015-0409.

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AbstractEvolution of bright optical spatial solitons in biased photovoltaic photorefractive (PVPR) medium is investigated in the present work. The space-charge field developed in the medium is comprised of local and nonlocal parts. Lowest order charge drift results in the buildup of the local space-charge field, whereas higher order drift and charge diffusion are responsible for nonlocal field development. The dynamical equation for solitons in the closed circuit PVPR medium is obtained under Akhmanov’s paraxial ray approximation. Conditions for stationary propagation are obtained, and the pat

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Kumar, Sachin, Brij Mohan, and Amit Kumar. "Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions." Physica Scripta 97, no. 3 (2022): 035201. http://dx.doi.org/10.1088/1402-4896/ac4f9d.

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Abstract This research aims to investigate a generalized fifth-order nonlinear partial differential equation for the Sawada-Kotera (SK), Lax, and Caudrey-Dodd-Gibbon (CDG) equations to study the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasma physics, and other nonlinear sciences. The Painlevé analysis is used to determine the integrability of the equation, and the simplified Hirota technique is applied to construct multiple soliton solutions with an investigation of the dispersion relation and phase shift of the equation. We utilize a linear combination approach to con

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Roslan, Muhammad Sufi, Kashif Tufail Chaudhary, Elham Mazalam, and Saktioto Saktioto. "Overview of Temporal Soliton Transmission on Photonic Crystal Fiber and Nanowires." Science, Technology and Communication Journal 1, no. 1 (2020): 16–19. http://dx.doi.org/10.59190/stc.v1i1.8.

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Solitons are nonlinear waves that exhibit persistent propagation in anomalous dispersion regime. In this article, we demonstrate the generation of soliton pulse in photonic crystal waveguide and nanowire at nonlinear length 6-mm in several photonic crystal waveguides and nanowire including fiber glass, silicon, silica, hollow photonic crystal and tellurite glass. Optical soliton pulse compression 0.5-ps with increasing order observed in this model. This study reveal propagation of soliton is feasible at high order mode in silicon nanowire (NW) and tellurite glass as compared with normal fiber

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Wang, Hui, and Tian-Tian Zhang. "Stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 3 (2019): 878–89. http://dx.doi.org/10.1108/hff-08-2018-0448.

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Purpose The purpose of this paper is to study stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms, which can be used to describe the propagation properties of optical soliton solutions. Design/methodology/approach The authors apply the ansatz method and the Hamiltonian system technique to find its bright, dark and Gaussian wave solitons and analyze its modulation instability analysis and stability analysis solution. Findings The results imply that the generalized nonlinear Schrödinger equation has bright, dark a

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Tan, Wei, and Miao Li. "Breather degeneration and lump superposition for the (3 + 1)-dimensional nonlinear evolution equation." Modern Physics Letters B 35, no. 15 (2021): 2150250. http://dx.doi.org/10.1142/s021798492150250x.

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This paper is devoted to the study of a (3 + 1)-dimensional generalized nonlinear evolution equation for the shallow-water waves. The breather solutions with different structures are obtained based on the bilinear form with perturbation parameters. Some new lump solitons are found in the process of studying the degradation behavior of breather solutions, and we also study general lump soliton, lumpoff solution and superposition phenomenon between lump soliton and breather solution. Besides, some theorems about the superposition between lump soliton and [Formula: see text]-soliton ([Formula: se

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Ren, Bo. "Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation." Advances in Mathematical Physics 2021 (April 9, 2021): 1–7. http://dx.doi.org/10.1155/2021/5545984.

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The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2 + 1 -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2 + 1 -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2 + 1 -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all

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Rahman, Muktarul, and Satyendra Nath Barman. "Existence of Small Amplitude KDV and MKDV Solitons in a Magnetized Dusty Plasma with q−Nonextensive Distributed Electrons." East European Journal of Physics, no. 2 (June 1, 2024): 74–89. http://dx.doi.org/10.26565/2312-4334-2024-2-06.

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The existence and propagating characteristics of small amplitude dust-ion-acoustic (DIA) Korteweg-de Vries (KdV) and modified KdV solitons in a three component magnetized plasma composed of positive inertial ions with pressure variation, noninertial electrons and negative charged immobile dust grains are theoretically and numerically investigated when the electrons obey a q-nonextensive velocity distribution. Utilizing the reductive perturbation method, to derive KdV and modified KdV equations and obtain the DIA soliton solutions along with the corresponding small amplitude potentials. This st

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Triki, Houria, and Abdul-Majid Wazwaz. "Bright and dark solitons for a generalized Korteweg-de Vries–modified Korteweg-de Vries equation with high-order nonlinear terms and time-dependent coefficients." Canadian Journal of Physics 89, no. 3 (2011): 253–59. http://dx.doi.org/10.1139/p11-015.

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We consider a generalized Korteweg-de Vries–modified Korteweg-de Vries (KdV–mKdV) equation with high-order nonlinear terms and time-dependent coefficients. Bright and dark soliton solutions are obtained by means of the solitary wave ansatz method. The physical parameters in the soliton solutions are obtained as functions of the varying model coefficients. Parametric conditions for the existence of envelope solitons are given. In view of the analysis, we see that the method used is an efficient way to construct exact soliton solutions for such a generalized version of the KdV–mKdV equation with

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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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Xu, Li-Jun, Zheng-Yi Ma, Jin-Xi Fei, Hui-Ling Wu, and Li Cheng. "The Multi-Soliton Solutions for the (2+1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation." Mathematics 13, no. 2 (2025): 236. https://doi.org/10.3390/math13020236.

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The (2+1)-dimensional integrable Caudrey–Dodd–Gibbon–Kotera–Sawada equation is a higher-order generalization of the Kadomtsev–Petviashvili equation, which can be applied in some physical branches such as the nonlinear dispersive phenomenon. In this paper, we first present the bilinear form for this equation after constructing one Bäcklund transformation. As a result, the one-soliton solution, two-soliton solution, and three-soliton solution are shown successively and the corresponding soliton structures are constructed. These solitons and their interactions illustrate that the obtained solutio

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Li, Longxing, Bitao Cheng, and Zhengde Dai. "The excitation of high-order localized waves in (3+1)-dimensional Kudryashov-Sinelshchikov equation." Physica Scripta 99, no. 3 (2024): 035214. http://dx.doi.org/10.1088/1402-4896/ad21ce.

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Abstract The aim of this work is to explore the excitation of high-order localized waves in the (3+1)-dimensional Kudryashov-Sinelshchikov equation, which is used to describe the dynamic of liquid with gas bubble. First of all, classical N-soliton solutions are constructed by means of Hirota bilinear form and symbolic calculation. What’s more, the high-order breather waves are derived through the degeneration process of the N-soliton solutions with conjugate parameter. Then, high-order lump waves are constructed by taking long wave limit technique on N-soliton solutions. Finally, the high-orde

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Xiao, Zhixing, Kang Li, and Junyi Zhu. "Multiple-Pole Solutions to a Semidiscrete Modified Korteweg-de Vries Equation." Advances in Mathematical Physics 2019 (May 2, 2019): 1–8. http://dx.doi.org/10.1155/2019/5468142.

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Multiple-pole soliton solutions to a semidiscrete modified Korteweg-de Vries equation are derived by virtue of the Riemann-Hilbert problem with higher-order zeros. A different symmetry condition is introduced to build the nonregular Riemann-Hilbert problem. The simplest multiple-pole soliton solution is presented. The dynamics of the solitons are studied.

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Konyukhov, A. I., and P. A. Mavrin. "Chirped soliton fission and fusion in dispersion oscillating fibers." Laser Physics 33, no. 1 (2022): 015401. http://dx.doi.org/10.1088/1555-6611/aca4cd.

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Abstract We found that pre-chirp of initial pulses allows to control both the fission and fusion of solitons in dispersion oscillating fiber characterized by a sinusoidally varying group velocity dispersion. The fission of second order solitons and collision of two co-propagated solitons are considered. It is shown that initial chirp can prevent the resonant fission of second order soliton into two pulses propagating with different group velocities. Inelastic collision of two in-phase solitons is found can be quite different, when the chirp imposed on initial pulses. The soliton transformation

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Radha, Ramaswamy, and Vaduganathan Ramesh Kumar. "Interplay Between Dispersion and Nonlinearity in Femtosecond Soliton Management." Zeitschrift für Naturforschung A 65, no. 6-7 (2010): 549–54. http://dx.doi.org/10.1515/zna-2010-6-710.

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In this paper, we investigate the inhomogeneous higher-order nonlinear Schr¨odinger (NLS) equation governing the femtosecond optical pulse propagation in inhomogeneous fibers using gauge transformation and generate bright soliton solutions from the associated linear eigenvalue problem. We observe that the amplitude of the bright solitons depends on the group velocity dispersion (GVD) and the self-phase modulation (SPM) while its velocity is dictated by the third-order dispersion (TOD) and GVD. We have shown how the interplay between GVD, SPM, and TOD can be profitably exploited to change solit

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Altun Durmuş, Selvi. "Optical soliton solutions of the higher-order nonlinear Schrödinger equation with Kerr law nonlinearity of self-phase modulation." Muş Alparslan Üniversitesi Fen Bilimleri Dergisi 13, no. 1 (2025): 37–45. https://doi.org/10.18586/msufbd.1636803.

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The primary aim of this article is to examine the higher-order nonlinear Schrödinger equation, which describes the propagation of dispersive pulses in fiber optics, characterized by self-phase modulation and Kerr law nonlinearity, and to employ the unified Riccati equation expansion method. Our objective is not only limited to obtaining various soliton solutions using the technique proposed in the article but also to investigate the impact of higher-order dispersion terms on soliton propagation in the examined model. New and significant physical features of the investigated model, influenced b

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Qiang, Long, Tristram J. Alexander, and C. Martijn de Sterke. "Solitons in media with mixed, high-order dispersion and cubic nonlinearity." Journal of Physics A: Mathematical and Theoretical, July 29, 2022. http://dx.doi.org/10.1088/1751-8121/ac8586.

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Abstract Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present analytic expressions for families of bright soliton solutions at arbitrary dispersion orders and practical methods to obtain the associated dispersion relations. These results provide a framework for considering higher order dispersion solitons and show the potential for further investigation of solitons in higher order dispersion systems.

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Al-Taie, Mohammed Salim Jasim. "Supercontinuum Generation by Controlling Pitch in Photonic Crystal Fibers." Sultan Qaboos University Journal for Science [SQUJS] 29, no. 1 (2024). http://dx.doi.org/10.53539/squjs.vol29iss1pp95-102.

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The influence of varying the distance between air holes (pitch) on the geography of solitone propagation through a photonic crystal fiber has been tested. The study depends on the Split-Step Fourier method and the results quantified using MATLAB. The first-order solitone was tested with the change in pitch, and it was found that there is a clear decay in the amplitude of the resulting pulse with an increase in pitch. When increasing the pitch in the case of second-order solitons, it was noticed that the pulse would split into multiple-order solitons down to higher-order solitons with the incre

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Zheng, Lu, Bo Tian, Dan-Yu Yang, and Yu-Qi Chen. "Resonance Y-type soliton and hybrid solutions for a (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system in a fluid or plasma." Modern Physics Letters B, July 20, 2023. http://dx.doi.org/10.1142/s0217984923501075.

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In this paper, a (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system in a fluid or plasma is investigated. Via the Hirota method and symbolic computation, we work out some two-resonance Y-type soliton solutions as well as some hybrid solutions composed of the two-resonance Y-type solitons and solitons/breathers. Graphically, we display some two-resonance Y-type solitons. We present the interactions between the two-resonance Y-type soliton and one soliton, among the two-resonance Y-type soliton and two solitons, between the two-resonance Y-type soliton and first-or

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Pei, Zhi-Jie, and Hai-Qiang Zhang. "Higher-order rational soliton solutions for the fifth-order modified KdV and KdV equations." International Journal of Modern Physics B, January 7, 2021, 2150036. http://dx.doi.org/10.1142/s0217979221500363.

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In this paper, we construct the generalized perturbation ([Formula: see text], [Formula: see text])-fold Darboux transformation of the fifth-order modified Korteweg-de Vries (KdV) equation by the Taylor expansion. We use this transformation to derive the higher-order rational soliton solutions of the fifth-order modified KdV equation. We find that these higher-order rational solitons admit abundant interaction structures. We graphically present the dynamics behaviors from the first- to fourth-order rational solitons. Furthermore, by the Miura transformation, we obtain the complex rational soli

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