Construction of multiple soliton solutions of the quintic nonlinear Schrodinger equation

TL;DR

This paper develops a method to explicitly construct multiple soliton solutions for an extended quintic nonlinear Schrödinger equation with higher-order dispersion and nonlinear terms, using spectral analysis and Riemann-Hilbert problem techniques.

Contribution

It introduces a novel approach to derive explicit multi-soliton solutions for a higher-order nonlinear Schrödinger equation via spectral analysis and Riemann-Hilbert problem formulation.

Findings

Explicit multi-soliton solutions are obtained.

The method applies to equations with higher-order dispersion and nonlinearities.

The solutions are constructed under zero boundary conditions.

Abstract

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.