arXiv subjects

Xiu-Bin Wang

Publications and source records attributed to Xiu-Bin Wang.

9 recordsLinked to original sources

arXiv2023

On the inverse scattering transform to the discrete Hirota equation with nonzero boundary conditions

Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral singularities. Using the inverse scattering transform method, we construct the Darboux transformation but not with the limit progress, which is more convenient than before. Several kinds of rational solutions are derived in detail. These solutions contain W-shape solitons, breathers, high-order rogue waves, and various interactions between solitons and breathers. Moreover, we analyze some remarkable characteristics of rational solutions through graphics. Our results are useful to explain the related nonlinear wave phenomena.

math-ph↗

arXiv2023

Characteristics of rogue waves in the scalar and vector nonlocal nonlinear Schrödinger equations

In this paper, general higher-order rogue wave solutions of the parity-time ($\mathcal {P}\mathcal {T}$) symmetric scalar and coupled nonlocal nonlinear Schrödinger equations (NLSEs) are calculated theoretically via a Darboux transformation by a separation of variable technique. Furthermore, in order to understand these solutions better, the main characteristics of the obtained solutions are explored clearly and conveniently. Our results show that the dynamics of these solutions exhibits rich patterns, most of which have no counterparts in the corresponding local equations.

math-ph↗

arXiv2023

Simple and high-order $N$-solitons of the nonlocal generalized Sasa-Satsuma equation via an improved Riemann-Hilbert method

In this paper, we investigate the nonlocal generalized Sasa-Satsuma (ngSS) equation based on an improved Riemann-Hilbert method (RHM). Different from the traditional RHM, the $t$-part of the Lax pair plays a more important role rather than the $x$-part in analyzing the spectral problems. So we start from the $t$-part of the spectral problems. In the process of dealing with the symmetry reductions, we are surprised to find that the computation is much less than the traditional RHM. We can more easily derive the compact expression of $N$-soliton solution of the ngSS equation under the reflectionless condition. In addition, the general high-order $N$-soliton solution of the ngSS equation is also deduced by means of the perturbed terms and limiting techniques. We not only demonstrate different cases for the dynamics of these solutions in detail in theory, but also exhibit the remarkable features of solitons and breathers graphically by demonstrating their 3D, projection profiles and wave propagations. Our results should be significant to understand the nonlocal nonlinear phenomena and provide a foundation for fostering more innovative research that advances the theory.

math-ph↗

arXiv2023

Inverse scattering transform of the general coupled Hirota system with nonzero boundary conditions

The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable, both the inverse and the direct problems are analyzed which allows us to develop the inverse scattering transform on the complex $z$-plane. Firstly, analyticity of the scattering eigenfunctions and scattering data, properties of the discrete spectrum, symmetries, and asymptotics are discussed in detail. Moreover, the inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is presented. Finally, the main characteristics of these obtained soliton solutions are graphically discussed in the $2\times2$ self-focusing case. This family of solutions contains novel Akhmediev breather and Kuznetsov-Ma soliton. These results would be of much importance in understanding and enriching breather wave phenomena arising in nonlinear and complex systems, especially in Bose-Einstein condensates.

math-ph↗

arXiv2021

Riemann-Hilbert problem of the three-component coupled Sasa-Satsuma equation and its multi-soliton solutions

In this work, the inverse scattering transform of the three-component coupled Sasa-Satsuma equation is investigated via the Riemann-Hilbert method. Firstly we consider a Lax pair associated with a $7\times 7$ matrix spectral problem for the equation. Then we present the spectral analysis of the Lax pair, from which a kind of Riemann-Hilbert problem is formulated. Moreover, $N$-soliton solutions to the equation are constructed through a particular Riemann-Hilbert problem with vanishing scattering coefficients. Finally, the dynamics of the soliton solutions are discussed with some graphics.

math.AP↗

arXiv2020

Long-time behavior for the Cauchy problem of the 3-component Manakov system

In this work, the Riemann-Hilbert problem for the 3-component Manakov system is formulated on the basis of the corresponding $4\times 4$ matrix spectral problem. Furthermore, by applying the nonlinear steepest descent techniques to an associated $4\times 4$ matrix valued Riemann-Hilbert problem, we can find leading-order asymptotics for the Cauchy problem of the 3-component Manakov system.

math.AP↗

arXiv2019

The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions

Under investigation in this work is the inverse scattering transform of the general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions (NZBCs), which can be reduced to several integrable equations. Firstly, a matrix Riemann-Hilbert problem for the equation with NZBCs at infinity is systematically investigated.Then the inverse problems are solved through the investigation of the matrix Riemann-Hilbert problem. Thus, the general solutions for the potentials, and explicit expressions for the reflection-less potentials are well constructed. Furthermore, the trace formulae and theta conditions are also presented. In particular, we analyze the simple-pole and double-pole solutions for the equation with NZBCs. Finally, the dynamics of the obtained solutions are graphically discussed. These results provided in this work can be useful to enrich and explain the related nonlinear wave phenomena in nonlinear fields.

math-ph↗

arXiv2019

Inverse scattering transform of an extended nonlinear Schrödinger equation with nonzero boundary conditions and its multisoliton solutions

Under investigation in this work is an extended nonlinear Schrödinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation with nonzero boundary conditions at infinity is systematically discussed. Then the inverse problems are solved through the investigation of the matrix Riemann-Hilbert problem. Therefore, the general solutions for the potentials, and explicit expressions for the reflection-less potentials are presented. Furthermore, we construct the simple-pole and double-pole solutions for the equation. Finally, the remarkable characteristics of these solutions are graphically discussed. Our results should be useful to enrich and explain the related nonlinear wave phenomena in nonlinear fields.

math-ph↗

arXiv2019

The nonlinear steepest descent approach for long time behavior of the two-component coupled Sasa-Satsuma equation with a $5\times 5$ Lax pair

Under investigation in this work is the coupled Sasa-Satsuma equation, which can describe the propagations of two optical pulse envelopes in birefringent fibers. The Riemann-Hilbert problem for the equation is formulated on the basis of the corresponding $5\times5$ matrix spectral problem, which allows us to present a suitable representation for the solution of the equation. Then the Deift-Zhou steepest descent method is used to analyze the long time behavior of the coupled Sasa-Satsuma equation.

math-ph↗