Annihilation Solitons and Chaotic Solitons for the （2＋1）-Dimensional Breaking Soliton System

By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.

Conservation Laws of a Discrete Soliton System

In this paper, we obtain an infinite number of conservation laws for a discrete soliton system by using a solvable generalized Riccati equation.

Chaotic Motion in a Harmonically Excited Soliton System

The influence of a soliton system under an external harmonic excitation is considered. We take the compound KdV-Burgers equation as an example, and investigate numerically the chaotic behavior of the system with a periodic forcing. Different routes to chaos such as period doubling, quasi-periodic routes, and the shapes of strange attractors are observed by using bifurcation diagrams, the largest Lyapunov exponents, phase projections and Poincaré maps.

Non-Traveling Wave Solutions for the (2+1)-Dimensional Breaking Soliton System

In this work, starting from the (G'/G)-expansion method and a variable separation method, a new non-traveling wave general solutions of the (2+1)-dimensional breaking soliton system are derived. By selecting appropriately the arbitrary functions in the solutions, special soliton-structure excitations and evolutions are studied.

Reinforcement Learning for Efficient Identification of Soliton System Parameters Across Expansive Domains

Optical solitons in mode-locked fiber lasers and optical communication links have various applications. Thestudy of transmission modes of optical solitons necessitates the investigation of the relationship between theequation parameters and soliton evolution employing deep learning techniques. However, the existing identificationmodels exhibit a limited parameter domain search range and are significantly influenced by initialization.Consequently, they often result in divergence toward incorrect parameter values. This study harnessed reinforcementlearning to revamp the iterative process of the parameter identification model. By developing a two-stageoptimization strategy, the model could conduct an accurate parameter search across arbitrary domains. Theinvestigation involved several experiments on various standard and higher-order equations, illustrating that theinnovative model overcame the impact of initialization on the parameter search, and the identified parametersare guided toward their correct values. The enhanced model markedly improves the experimental efficiency andholds significant promise for advancing the research of soliton propagation dynamics and addressing intricatescenarios.

Nondegenerate Soliton Solutions of(2+1)-Dimensional Multi-Component Maccari System

For a multi-component Maccari system with two spatial dimensions,nondegenerate one-soliton and two-soliton solutions are obtained with the bilinear method.It can be seen by drawing the spatial graphs of nondegenerate solitons that the real component of the system shows a cross-shaped structure,while the two solitons of the complex component show a multi-solitoff structure.At the same time,the asymptotic analysis of the interaction behavior of the two solitons is conducted,and it is found that under partially nondegenerate conditions,the real and complex components of the system experience elastic collision and inelastic collision,respectively.

Analytical Method for Designing Grating Compensated Dispersion-Managed Soliton Systems

We show a useful analytical method to design grating compensated dispersion-managed systems. Our method is in good agreement with the numerical results even in the presence of group delay ripples in the chirped fiber gratings.

Filter control polarization mode dispersion in dispersion managed soliton systems

In this paper, the dispersion managed soliton (DMS) transmission equation is built on considering the effects of polarization mode dispersion (PMD) and filter control. The DMS transmission of filtering control in constant birefringence fibers is firstly analyzed by varitional method, from which the evolving rules of characteristical DMS parameters are obtained. Secondly, the stability of DMS transmission and its timing jitter are investigated in the random varying birefringence fibers with the conventional model of PMD. The results reveal that filter control DMS system has powerful robustness to PMD effects and DMS's timing jitter can be decreased considerably with the help of filters.

EVOLUTION OF THE SCATTERING DATA UNDER THE CLASSICAL DARBOUX TRANSFORM FOR su(2) SOLITON SYSTEMS

The changing of the scattering data for the solutions of su (2) soliton systems which are relatedby a classical Darboux transformation (CDT) is obtained. It is shown that how a CDT creates anderases a soliton.

Soliton solution and interaction property for a coupled modified Korteweg-de Vries (mKdV) system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.

RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS

Based on a 4 x 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken.

N SOLITON SOLUTION FOR A CLASS OF THE SYSTEM OF LS NONLINEAR WAVE INTERACTION

In this note,the explicit form of the N soliton solutions for a class of the system of LS nonlinear wave interaction have been obtained by using Hirota's method.

Collision-induced timing jitter in dispersion-managed WDM soliton system with filtering

Taking into account the randomicity of collision positions and the arbitrary encoding of data in channel, the influences of different dispersion management on collision-induced timing jitter in a filtered wavelength division multiplexing (WDM) soliton system are obtained statistically and numerically by applying a set of coupled ordinary differential equations which are derived through variational procedure. The optimal dispersion managements which can greatly reduce the collision-induced timing jitter are found. The multi-channel collision-induced timing jitters in a filtered WDM soliton system are given with an optimal dispersion management and constant dispersion.

Fusion and fission solitons for the (2+1)-dimensional generalized Breor-Kaup system

With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions （including solitory wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （2＋1）-dimensional generalized Breor-Kaup （GBK） system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons.

Soliton-like pulse timing jitter in dispersion-managed systems

In this paper, the timing jitter in dispersion-managed soliton-like systems with the Caussian pulse is studied by using two methods. Firstly, the derivation of the dynamic equations for the evolution of soliton-like parameters and the timing jitter expressions for the dispersion-managed soliton-like systems are carried out by the perturbed variational method. By analysing and simulating these timing jitter expressions, one can find that the timing jitter is induced by the amplified spontaneous emission noise and the frequency shift, etc. Nonlinear gain can suppress the timing jitter. The chirp sign and the filters action have also effects on the total timing jitter. Secondly, the timing jitter is calculated and analysed by using the moment method. The results of the two methods prove to be consistent with each other.

Instantaneous solitons and fractal solitons for a (2+1)-dimensional nonlinear system

By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.

Soliton Solutions of Coupled KdV System from Hirota's Bilinear Direct Method

With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.

Exotic interactions between solitons of the （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov system

Starting from the extended tanh-function method （ETM） based on the mapping method, the variable separation solutions of the （2＋1）-dimensional asymmetric Nizhnik Novikov Veselov （ANNV） system are derived. By further study, we find that these variable separation solutions are seemingly independent of but actually dependent on each other. Based on the variable separation solution and by choosing appropriate functions, some novel and interesting interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semifoldon, are investigated.

Evolution and Stability of Dark Holographic Solitons in Photorefractive Dissipative Systems

The dynamics evolution of dark holographic solutions in a dissipative system is investigated numerically provided that the double balance, i.e. diffraction is balanced by nonlinearity and loss is balanced by gain, is satisfied. The influence of the system parameters, such as the linear loss of the crystal, the external biased field and the angel between input beams, on the stable propagation of soliton beams is discussed numerically. Results show that such solitons can be easily amplified or absorbed by adjusting these system parameters. Furthermore, numerical simulations indicate that dissipative dark holographic solitons are stable for small perturbation on amplitude.

The influence of stochastic dispersion on optical soliton system and its suppression

The influence of stochastic dispersion on an optical soliton communication system is investigated, and the method of reducing this influence is also given. The analysis shows that the existence-of stochastic dispersion results in the arrival time jitter, which is in proportion to the mean square fluctuation of the imaginary component of stochastic dispersion and is related to soliton amplitude and velocity. The influence of stochastic dispersion can be reduced by using filtering method in frequency domain.