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Journal articles on the topic 'Solitons'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Aycock, Lauren M., Hilary M. Hurst, Dmitry K. Efimkin, et al. "Brownian motion of solitons in a Bose–Einstein condensate." Proceedings of the National Academy of Sciences 114, no. 10 (2017): 2503–8. http://dx.doi.org/10.1073/pnas.1615004114.

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We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongatedRb87Bose–Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton’s diffusive behavior using a quasi-1D sc

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2

Segovia, Francis Armando, and Emilse Cabrera. "SOLUCIÓN DE LA ECUACIÓN NO LINEAL DE SCHRODINGER (1+1) EN UN MEDIO KERR." Redes de Ingeniería 6, no. 2 (2015): 26. http://dx.doi.org/10.14483/udistrital.jour.redes.2015.2.a03.

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Se presenta un marco teórico y se muestra una simulación numérica de la propagación de solitones. Con especial atención a los solitones ópticos espaciales, se calcula analíticamente el perfil de solitón correspondiente a la ecuación Schrodinger no-lineal para un medio Kerr. Los resultados muestran que los solitones ópticos son pulsos estables cuya forma y espectro son preservados en grandes distancias.Solution of the nonlinear Schrodinger equation (1+1) in a Kerr mediumABSTRACTThis document presents a theoretical framework and shows a numerical simulation for the propagation of solitons. With

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3

Zhao, Xue-Hui, Bo Tian, Yong-Jiang Guo, and Hui-Min Li. "Solitons interaction and integrability for a (2+1)-dimensional variable-coefficient Broer–Kaup system in water waves." Modern Physics Letters B 32, no. 08 (2018): 1750268. http://dx.doi.org/10.1142/s0217984917502682.

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Under investigation in this paper is a (2+1)-dimensional variable-coefficient Broer–Kaup system in water waves. Via the symbolic computation, Bell polynomials and Hirota method, the Bäcklund transformation, Lax pair, bilinear forms, one- and two-soliton solutions are derived. Propagation and interaction for the solitons are illustrated: Amplitudes and shapes of the one soliton keep invariant during the propagation, which implies that the transport of the energy is stable for the (2+1)-dimensional water waves; and inelastic interactions between the two solitons are discussed. Elastic interactio

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4

GONZÁLEZ, JORGE A., and JOSE R. CARBÓ. "STATIONARITY-BREAKING BIFURCATIONS OF SOLITONS UNDER NONLINEAR DAMPING." Modern Physics Letters B 08, no. 12 (1994): 739–48. http://dx.doi.org/10.1142/s0217984994000741.

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The existence and dynamics of solitons in general systems with nonlinear damping are investigated. The mechanism of a new bifurcation after which the soliton can no longer be in a stationary state is discussed. Some particular cases are studied in detail and exact solutions are presented. The possibility and importance of self-sustained solitons, solitonic limit cycles, and chaotic solitons in these systems are analyzed.

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5

Meng, Yong, Hafiz Wajahat Ahmed Riaz, and Ji Lin. "New types of nondegenerate solitons for a (2+1)-dimensional coupled system*." Communications in Theoretical Physics 77, no. 9 (2025): 095001. https://doi.org/10.1088/1572-9494/adc240.

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Abstract In this paper, we investigate the (2+1)-dimensional three-component long-wave-short-wave resonance interaction system, which describes complex systems and nonlinear wave phenomena in physics. By employing the Hirota bilinear method, we derive the general nondegenerate N-soliton solution of the system, where each short-wave component contains N arbitrary functions of the independent variable y. The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types. Finally, we illustrate the structural features of se

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6

Xiao, Zi-Jian, Bo Tian, and Yan Sun. "Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics." Modern Physics Letters B 32, no. 02 (2018): 1750170. http://dx.doi.org/10.1142/s0217984917501706.

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In this paper, we investigate a (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons a

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7

Peng, Yangyang, Guangyu Xu, Keyun Zhang, Meisong Liao, Yongzheng Fang, and Yan Zhou. "Modulating anti-dark vector solitons." Laser Physics 33, no. 9 (2023): 095101. http://dx.doi.org/10.1088/1555-6611/ace251.

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Abstract Theoretical analysis of the modulation of anti-dark vector solitons is conducted in this work. The simulation depends on a single-mode optical fiber out-cavity modulation system model that works at 1 μm. The anti-dark vector soliton’s initial state is assumed to be polarization-/group-velocity-locked, with same/different central wavelengths in orthogonally polarized directions. After soliton parameter modulation, modulated anti-dark vector solitons at the output port will demonstrate different properties in orthogonal directions. For example, two symmetrically located frequency peaks

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8

Zhang, Ling-Ling, and Xiao-Min Wang. "Bright–dark soliton dynamics and interaction for the variable coefficient three-coupled nonlinear Schrödinger equations." Modern Physics Letters B 34, no. 05 (2019): 2050064. http://dx.doi.org/10.1142/s0217984920500645.

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Under investigation in this paper is the variable coefficient three-coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of solitonic excitations along three-spine [Formula: see text]-helical protein with inhomogeneous effect. Via the Hirota method and symbolic computation, the exact two-bright-one-dark (TBD) and one-bright-two-dark (BTD) soliton solutions are constructed analytically. The propagation properties are discussed for TBD and BTD solitons when the variable coefficient is a hyperbolic secant function. Figures are plotted to reveal the following interactions of T

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9

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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10

Singh, Abhishek, та Shyam Kishor. "SOME TYPES OF η-RICCI SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS". Facta Universitatis, Series: Mathematics and Informatics 33, № 2 (2018): 217. http://dx.doi.org/10.22190/fumi1802217s.

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In this paper we study some types of η-Ricci solitons on Lorentzianpara-Sasakian manifolds and we give an example of η-Ricci solitons on 3-dimensional Lorentzian para-Sasakian manifold. We obtain the conditions of η-Ricci soliton on ϕ-conformally flat, ϕ-conharmonically flat and ϕ-projectivelyflat Lorentzian para-Sasakian manifolds, the existence of η-Ricci solitons implies that (M,g) is η-Einstein manifold. In these cases there is no Ricci solitonon M with the potential vector field

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11

Ivanov, S. K., and A. M. Kamchatnov. "Motion of dark solitons in a non-uniform flow of Bose–Einstein condensate." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 11 (2022): 113142. http://dx.doi.org/10.1063/5.0123514.

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We study motion of dark solitons in a non-uniform one-dimensional flow of a Bose–Einstein condensate. Our approach is based on Hamiltonian mechanics applied to the particle-like behavior of dark solitons in a slightly non-uniform and slowly changing surrounding. In one-dimensional geometry, the condensate’s wave function undergoes the jump-like behavior across the soliton, and this leads to generation of the counterflow in the background condensate. For a correct description of soliton’s dynamics, the contributions of this counterflow to the momentum and energy of the soliton are taken into ac

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12

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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13

LIANG, Z. X., and Z. D. ZHANG. "EXACT SOLITONS IN THE GROSS–PITAEVSKII EQUATION WITH TIME-MODULATED NONLINEARITY." Modern Physics Letters B 21, no. 07 (2007): 383–90. http://dx.doi.org/10.1142/s0217984907012864.

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Exact solitonic solutions of the Gross–Pitaevskii equation with time-modulated nonlinearity of a(t) = a0 / (t + t0) are obtained. With help of these solutions, we analyze the properties of Feshbach-managed solitons in Bose–Einstein condensates in details. Our results show that the parameters of atomic matter waves can be manipulated by proper variation of the scattering length. In particular, an exact two-soliton solution is given, from which, it is shown that the separation between the neighboring solitons can be effectively maintained by allowing the solitons to have unequal initial amplitud

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14

Bo, Wen-Bo, Ru-Ru Wang, Wei Liu, and Yue-Yue Wang. "Symmetry breaking of solitons in the PT-symmetric nonlinear Schrödinger equation with the cubic–quintic competing saturable nonlinearity." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 9 (2022): 093104. http://dx.doi.org/10.1063/5.0091738.

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The symmetry breaking of solitons in the nonlinear Schrödinger equation with cubic–quintic competing nonlinearity and parity-time symmetric potential is studied. At first, a new asymmetric branch separates from the fundamental symmetric soliton at the first power critical point, and then, the asymmetric branch passes through the branch of the fundamental symmetric soliton and finally merges into the branch of the fundamental symmetric soliton at the second power critical point, while the power of the soliton increases. This leads to the symmetry breaking and double-loop bifurcation of fundamen

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15

Castro, Camilo J., and Deterlino Urzagasti. "Seesaw drift of bright solitons of the nonlinear Schrödinger equation with a periodic potential." Journal of Nonlinear Optical Physics & Materials 25, no. 03 (2016): 1650038. http://dx.doi.org/10.1142/s0218863516500387.

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Soliton solutions are investigated employing the nonlinear Schrödinger equation (NLSE) with an additional term corresponding to an external periodic field. In particular, we use this equation to describe the behavior of solitons in fiber optics in the case of anomalous dispersion. Employing the framework of variational analysis and analytical approximations, single peaked soliton solutions are derived, which exhibit variations of the solitonic parameters due to the effect of the periodic potential and a harmonic oscillator motion of the soliton center, when the frequency of the external field

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16

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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17

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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18

Gong, Junsheng, and Jiancheng Liu. "Rigidity Characterizations of Conformal Solitons." Mathematics 13, no. 11 (2025): 1837. https://doi.org/10.3390/math13111837.

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We study the rigidity of conformal solitons, give a sufficient and necessary condition that guarantees that every closed conformal soliton is gradient conformal soliton, and prove that complete conformal solitons with a nonpositive Ricci curvature must be trivial under an integral condition. In particular, by using a p-harmonic map from a complete gradient conformal soliton in a smooth Riemannian manifold, we classify complete noncompact nontrivial gradient conformal solitons under some suitable conditions, and similar results are given for gradient Yamabe solitons and gradient k-Yamabe solito

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19

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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20

Seadawy, Aly R., and Mujahid Iqbal. "Optical soliton solutions for nonlinear complex Ginzburg–Landau dynamical equation with laws of nonlinearity Kerr law media." International Journal of Modern Physics B 34, no. 19 (2020): 2050179. http://dx.doi.org/10.1142/s0217979220501799.

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In this research article, our aim is to construct new optical soliton solutions for nonlinear complex Ginzburg–Landau equation with the help of modified mathematical technique. In this work, we studied both laws of nonlinearity (Kerr and power laws). The obtained solutions represent dark and bright solitons, singular and combined bright-dark solitons, traveling wave, and periodic solitary wave. The determined solutions provide help in the development of optical fibers, soliton dynamics, and nonlinear optics. The constructed solitonic solutions prove that the applicable technique is more reliab

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21

Aquib, Md, Oğuzhan Bahadır, Laltluangkima Chawngthu, and Rajesh Kumar. "Geometric and Structural Properties of Indefinite Kenmotsu Manifolds Admitting Eta-Ricci–Bourguignon Solitons." Mathematics 13, no. 12 (2025): 1965. https://doi.org/10.3390/math13121965.

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This paper undertakes a detailed study of η-Ricci–Bourguignon solitons on ϵ-Kenmotsu manifolds, with particular focus on three special types of Ricci tensors: Codazzi-type, cyclic parallel and cyclic η-recurrent tensors that support such solitonic structures. We derive key curvature conditions satisfying Ricci semi-symmetric (R·E=0), conharmonically Ricci semi-symmetric (C(ξ,βX)·E=0), ξ-projectively flat (P(βX,βY)ξ=0), projectively Ricci semi-symmetric (L·P=0) and W5-Ricci semi-symmetric (W(ξ,βY)·E=0), respectively, with the admittance of η-Ricci–Bourguignon solitons. This work further explore

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Sarkar, Avijit, and Urmila Biswas. "Riemann solitons on perfect fluid spacetimes." Filomat 38, no. 33 (2024): 11773–84. https://doi.org/10.2298/fil2433773s.

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In this article, we characterize Riemann solitons on perfect fluid spacetimes. Some relationship between perfect fluid spacetimes and Riemann solitons with certain soliton vector fields are established. We investigate Ricci-symmetric perfect fluid spacetimes whose metrics are Riemann solitons. Pseudo-projectively flat perfect fluid spacetimes with the metrics as Riemann solitons have been studied. It is also proved that a gradient Riemann soliton on a perfect fluid spacetime is Einstein. An example of a gradient Riemann soliton on perfect fluid spacetime has been constructed.

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23

Polyakov, Sergey, and Anatoly Sukhorukov. "Gap solitons." Izvestiya VUZ. Applied Nonlinear Dynamics 6, no. 4 (1998): 45–56. http://dx.doi.org/10.18500/0869-6632-1998-6-4-45-56.

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In this paper we present the studies of the problem of slow and immobile solitons which are excited inside the stop bands of inhomogeneous media with either quadratic or cubic nonlinearity. We found an integral criterion of slow soliton formation, determined the main properties of gар solitons. The dynamics of parametric gap soliton formation and propagation in quadratic media is illustrated by means of computer simulations and compared with such solitons due to cubic nonlinearity.

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Yao, Y., C. J. Luo, X. X. Wang, and H. Zhang. "Research on solitons’ interactions in one-dimensional indium chains on Si(111) surfaces." Journal of Physics: Conference Series 2639, no. 1 (2023): 012051. http://dx.doi.org/10.1088/1742-6596/2639/1/012051.

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Abstract Solitons have garnered significant attention across various fields, yet a contentious debate persists regarding the precise structure of solitons on indium chains. Currently, multiple forms of solitons in one-dimensional atomic chains have been reported. STM provides an effective means to study the precise atomic structure of solitons, particularly their dynamics and interactions. However, limited research has been conducted on soliton interactions and soliton-chain interactions, despite their profound impact on relative soliton motions and the overall physical properties of the syste

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25

Zhao, Chen, Yi-Tian Gao, Zhong-Zhou Lan, Jin-Wei Yang, and Chuan-Qi Su. "Bilinear forms and dark-soliton solutions for a fifth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber." Modern Physics Letters B 30, no. 24 (2016): 1650312. http://dx.doi.org/10.1142/s0217984916503127.

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In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation is investigated, which describes the propagation of the attosecond pulses in an optical fiber. Via the Hirota’s method and auxiliary functions, bilinear forms and dark one-, two- and three-soliton solutions are obtained. Propagation and interaction of the solitons are discussed graphically: We observe that the solitonic velocities are only related to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the coefficients of the second-, third-, fourth- and fifth-order terms, respect

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Sun, Yan, Bo Tian, Hui-Ling Zhen, Xiao-Yu Wu, and Xi-Yang Xie. "Soliton solutions for a (3 + 1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a plasma." Modern Physics Letters B 30, no. 20 (2016): 1650213. http://dx.doi.org/10.1142/s0217984916502134.

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Under investigation in this paper is a (3 + 1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Hirota method and symbolic computation, we obtain the one-, two- and three-soliton solutions for such an equation. We graphically study the solitons related with the coefficient of the cubic nonlinearity [Formula: see text]. Amplitude of

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Ma, Lei-Nuo, Si Li, Tian-Mu Wang, Xi-Yang Xie, and Zhong Du. "Multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations via Riemann-Hilbert approach." Physica Scripta 98, no. 7 (2023): 075222. http://dx.doi.org/10.1088/1402-4896/acde12.

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Abstract In this paper, we study multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fibers. We analyze the spectrum of the Lax pair to establish the Riemann-Hilbert problem. Using such Riemann-Hilbert problem, we calculate various multi-soliton solutions without reflection, including breather-like and mixed solitons. We illustrate the propagation and interaction dynamics of the solitons through appropriate parameter selection and a

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28

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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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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Sardar, Arpan, Changhwa Woo, and Uday De. "Almost Schouten solitons and contact geometry." Filomat 38, no. 32 (2024): 11295–308. https://doi.org/10.2298/fil2432295s.

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The current article is about almost Schouten solitons and gradient Schouten solitons on contact geometry. At first, we demonstrate that if a compact K-contact manifold admits an almost Schouten soliton, then the soliton is shrinking and the manifold is an Einstein manifold. Moreover, we show that if a K-contact manifold admits a gradient Schouten soliton, then the manifold becomes an Einstein manifold. Next, we investigate almost Schouten solitons and gradient Schouten solitons on (k, ?)-contact manifolds. Finally, we show that if a complete H-contact manifold2n+1 M satisfying certain restrict

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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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32

Hammad, A., T. D. Swinburne, H. Hasan, S. Del Rosso, L. Iannucci, and A. P. Sutton. "Theory of the deformation of aligned polyethylene." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (2015): 20150171. http://dx.doi.org/10.1098/rspa.2015.0171.

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Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel–Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the introduction of tensile and compressive solitons at the chain ends to mark the onset of plasticity at a well-defined yield stress, which is much less than the theoretical pull-out stress. Interaction energies

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33

Li, Dong, Ruizhan Zhai, Yongjing Wu, et al. "The Study of Soliton Mode-Locked and Bound States in Erbium-Doped Fiber Lasers Based on Cr2S3 Saturable Absorbers." Materials 18, no. 4 (2025): 864. https://doi.org/10.3390/ma18040864.

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Femtosecond fiber lasers are widely utilized across various fields and also serve as an ideal platform for studying soliton dynamics. Bound-state solitons, as a significant soliton dynamic phenomenon, attract widespread attention and research interest because of their potential applications in high-speed optical communication, all-optical information storage, quantum computing, optical switching, and high-resolution spectroscopy. We investigate the effects of pump power variations on the formation of mode-locked solitons and bound-state solitons in a femtosecond fiber laser with a Cr2S3 satura

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34

Deshmukh, Sharief, and Hana Alsodais. "A Note on Ricci Solitons." Symmetry 12, no. 2 (2020): 289. http://dx.doi.org/10.3390/sym12020289.

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In this paper, we characterize trivial Ricci solitons. We observe the important role of the energy function f of a Ricci soliton (half the squared length of the potential vector field) in the charectrization of trivial Ricci solitons. We find three characterizations of connected trivial Ricci solitons by imposing different restrictions on the energy function. We also use Hessian of the potential function to characterize compact trivial Ricci solitons. Finally, we show that a solution of a Poisson equation is the energy function f of a compact Ricci soliton if and only if the Ricci soliton is t

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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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Konyukhov, Andrey I. "Transformation of Eigenvalues of the Zakharov–Shabat Problem under the Effect of Soliton Collision." Izvestiya of Saratov University. New series. Series: Physics 20, no. 4 (2020): 248–57. http://dx.doi.org/10.18500/1817-3020-2020-20-4-248-257.

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Background and Objectives: The Zakharov–Shabat spectral problem allows to find soliton solutions of the nonlinear Schrodinger equation. Solving the Zakharov–Shabat problem gives both a discrete set of eigenvalues λj and a continuous one. Each discrete eigenvalue corresponds to an individual soliton with the real part Re(λj) providing the soliton velocity and the imaginary part Im(λj) determining the soliton amplitude. Solitons can be used in optical communication lines to compensate both non-linearity and dispersion. However, a direct use of solitons in return-to-zero signal encoding is inhibi

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Bhrawy, A. H., A. A. Alshaery, E. M. Hilal, Wayne N. Manrakhan, Michelle Savescu, and Anjan Biswas. "Dispersive optical solitons with Schrödinger–Hirota equation." Journal of Nonlinear Optical Physics & Materials 23, no. 01 (2014): 1450014. http://dx.doi.org/10.1142/s0218863514500143.

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The dynamics of dispersive optical solitons, modeled by Schrödinger–Hirota equation, are studied in this paper. Bright, dark and singular optical soliton solutions to this model are obtained in presence of perturbation terms that are considered with full nonlinearity. Soliton perturbation theory is also applied to retrieve adiabatic parameter dynamics of bright solitons. Optical soliton cooling is also studied. Finally, exact bright, dark and singular solitons are addressed for birefringent fibers with perturbation terms included.

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He, Feng-Tao, Xiao-Lin Wang, and Zuo-Liang Duan. "The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber." Scientific World Journal 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/130734.

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We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term

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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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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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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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Xie, Xi-Yang, and Gao-Qing Meng. "Dark-soliton collisions for a coupled AB system in the geophysical fluids or nonlinear optics." Modern Physics Letters B 32, no. 04 (2018): 1850039. http://dx.doi.org/10.1142/s0217984918500392.

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Under investigation in this paper is a coupled AB system, which describes the marginally unstable baroclinic wave packets in the geophysical fluids or ultra-short pulses in nonlinear optics. As the dark solitons are more resistant against various perturbations than the bright ones, we aim to investigate the dark solitons in the geophysical fluids or nonlinear optics. Dark one- and two-soliton solutions for such a system are derived based on the bilinear forms and propagations of the one solitons and collisions between the two solitons are graphically illustrated and analyzed. Further, influenc

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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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Prasad, Rajendra, та Vinay Kumar. "Kenmotsu 3-manifold admitting gradient Ricci-Yamabe solitons and *-η-Ricci-Yamabe solitons". Filomat 38, № 13 (2024): 4569–83. https://doi.org/10.2298/fil2413569p.

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In this paper, we classify Kenmotsu manifolds admitting gradient Ricci-Yamabe solitons and *-?-Ricci-Yamabe solitons. We find conditions of Kenmotsu manifold about when it shrink, expand and steady. It is shown that Kenmotsu 3-manifold endowed with gradient Ricci-Yamabe soliton and with constant scalar curvature becomes an Einstein manifold. We, also study Kenmotsu manifold admitting *-?-Ricci-Yamabe solitons becomes generalized ?-Einstein manifold and the curvature condition R.S = 0. Finally, we provide two examples which proves existence of gradient Ricci-Yamabe soliton and *-?-Ricci-Yamabe

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Hong, Woo-Pyo. "Dynamics of Pulsating, Erupting, and Creeping Solitons in the Cubic- Quintic Complex Ginzburg-Landau Equation under the Modulated Field." Zeitschrift für Naturforschung A 61, no. 10-11 (2006): 525–35. http://dx.doi.org/10.1515/zna-2006-10-1103.

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It is shown that the dynamics of the pulsating, erupting, and creeping (PEC) solitons in the one-dimensional cubic-quintic complex Ginzburg-Landau equation can be drastically modified in the presence of a modulated field. We first perform the linear instability analysis of continuous-wave (CW) and obtain the gain by the modulational instability (MI). It is found that the CW states applied by the weakly modulated field always transform into fronts for the parameters of the PEC solitons. We then show that, when the modulated field is applied to the pulse-like initial profile, multiple solitons a

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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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Hussain, Ibrar, Tahirullah, and Suhail Khan. "Four-dimensional Lorentzian plane symmetric static Ricci solitons." International Journal of Modern Physics D 28, no. 16 (2019): 2040010. http://dx.doi.org/10.1142/s0218271820400106.

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Our focus is to investigate the Ricci solitons of the plane symmetric and static four-dimensional Lorentzian metrics. It is found that these metrics admit shrinking and concircular potential Ricci soliton vector fields with either 6- or 10-dimensional Lie algebra. Further, it is observed that the 4-dimensional Lorentzian static Ricci soliton manifolds are Einsteinian and hence the Ricci solitons are the trivial Ricci solitons.

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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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Siddiqi, Mohd Danish, and Fatemah Mofarreh. "Hyperbolic Ricci soliton and gradient hyperbolic Ricci soliton on relativistic prefect fluid spacetime." AIMS Mathematics 9, no. 8 (2024): 21628–40. http://dx.doi.org/10.3934/math.20241051.

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<p>In this research note, we investigated the characteristics of perfect fluid spacetime when coupled with the hyperbolic Ricci soliton. We additionally interacted with the perfect fluid spacetime, with a $ \varphi(\mathcal{Q}) $-vector field and a bi-conformal vector field that admits the hyperbolic Ricci solitons. Furthermore, we analyze the gradient hyperbolic Ricci soliton in perfect fluid spacetime, employing a scalar concircular field, and discuss about the gradient hyperbolic Ricci soliton's rate of change. In the end, we determined the energy conditions for perfect fluid spacetim

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Wang, Dikai. "Generalized solitons: Resize the amplitudes of solitons." Journal of Physics: Conference Series 2964, no. 1 (2025): 012080. https://doi.org/10.1088/1742-6596/2964/1/012080.

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Abstract A classical soliton is a solitary wave whose amplitude, shape, and velocity remain unchanged. The letter discovers a novel property of a soliton to change its amplitude. Simulations show that: (1) The amplitude of each soliton can be changed by exerting a function on it. The classical soliton affected by the function is extended to a generalized soliton. (2) The generalized soliton retains the properties of the function. (3) Many generalized solitons can be easily constructed by using different functions.

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