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

TL;DR

This paper applies the Riemann-Hilbert method to derive N-soliton solutions for an eighth-order nonlinear Schrödinger equation relevant in optical fibers, demonstrating localized wave structures and dynamics.

Contribution

It introduces a Riemann-Hilbert framework for solving the eighth-order nonlinear Schrödinger equation and constructs explicit N-soliton solutions in the reflectionless case.

Findings

Explicit N-soliton solutions are obtained.

Localized structures are visualized through plots.

Dynamic behaviors of solitons are analyzed.

Abstract

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.