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

TL;DR

This paper develops a Riemann-Hilbert approach to derive multi-soliton solutions for a fifth-order nonlinear Schrödinger equation modeling ferromagnetic spin chains, revealing detailed soliton structures and dynamics.

Contribution

It introduces a systematic method using Riemann-Hilbert problems to obtain multisoliton solutions for the fifth-order nonlinear Schrödinger equation.

Findings

Explicit multisoliton solutions derived

Visualization of soliton structures and dynamics

Application to ferromagnetic spin chain model

Abstract

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.