arXiv subjects

Tie-Cheng Xia

Publications and source records attributed to Tie-Cheng Xia.

5 recordsLinked to original sources

arXiv2020

Construction of multiple soliton solutions of the quintic nonlinear Schrodinger equation

In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral analysis, a kind of matrix Riemann-Hilbert problem is formulated on the real axis. Then on basis of the resulting matrix Riemann-Hilbert problem under restriction of no reflection, multiple soliton solutions of the extended nonlinear Schrodinger equation are generated explicitly.

nlin.SI↗

arXiv2019

Constructing Riemann-Hilbert problem and multi-soliton solutions for the N-coupled Hirota equations in an optical fiber

This paper focuses on investigation of the N-coupled Hirota equations arising in an optical fiber. Starting from analyzing the spectral problem, a kind of matrix Riemann-Hilbert problem is formulated strictly on the real axis. Then based on the resulting matrix Riemann-Hilbert problem under the constraint of no reflection, multi-soliton solutions to the N-coupled Hirota equations are presented explicitly.

math-ph↗

arXiv2018

Riemann-Hilbert method for N-soliton solution of the coupled Hirota system in nonlinear fiber

Under investigation in this work is the coupled Hirota system arising in nonlinear fiber. The spectral analysis of the Lax pair is first carried out and a Riemann-Hilbert problem is described. Then in the framework of the obtained Riemann-Hilbert problem with the reflectionless case, N-soliton solution is presented for the coupled Hirota system. Finally, via proper choices of the involved parameters, a few plots are made to exhibit the localized structures and dynamic characteristics of one-soliton solution.

math-ph↗

arXiv2018

Riemann-Hilbert approach for multi-soliton solutions of a fifth-order nonlinear Schrodinger equation

A fifth-order nonlinear Schrodinger equation which describes one-dimensional anisotropic Heisenberg ferromagnetic spin chain is under exploration in this paper. Starting from the spectral analysis of the Lax pair, a Riemann-Hilbert problem is set up. After solving the obtained Riemann-Hilbert problem with reflectionless case, we systematically derive multisoliton solutions for the fifth-order nonlinear Schrodinger equation. In addition, the localized structures and dynamic behaviors of one- and two-soliton solutions are shown vividly via a few plots.

math-ph↗

arXiv2018

Riemann-Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrodinger equation in an optical fiber

This paper aims to present an application of Riemann-Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrodinger equation arising in an optical fiber. Starting from the spectral analysis of the Lax pair, a Riemann-Hilbert problem is formulated. Then by solving the obtained Riemann-Hilbert problem under the reflectionless case, N-soliton solution is generated for the eighth-order nonlinear Schrodinger equation. Finally, the three-dimensional plots and two-dimensional curves with specific choices of the involved parameters are made to show the localized structures and dynamic behaviors of one- and two-soliton solutions.

math-ph↗