On multi-soliton solutions to a generalized inhomogeneous nonlinear Schrodinger equation for the Heisenberg ferromagnetic spin chain

TL;DR

This paper derives explicit multi-soliton solutions for a generalized inhomogeneous higher-order nonlinear Schrödinger equation related to the Heisenberg ferromagnetic spin chain, using spectral analysis and Riemann-Hilbert problem techniques.

Contribution

It introduces a method to obtain explicit multi-soliton solutions for the GIHNLS equation via spectral analysis and Riemann-Hilbert problem formulation.

Findings

Explicit multi-soliton solutions derived

One- and two-soliton solutions analyzed visually

Method applicable to similar integrable systems

Abstract

A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis is first performed to generate a related matrix Riemann-Hilbert problem on the real axis. Then, through solving the resulting matrix Riemann-Hilbert problem by taking the jump matrix to be the identity matrix, the general bright multi-soliton solutions to the GIHNLS equation are attained. Furthermore, the one- and two-soliton solutions are written out and analyzed by figures.