Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

TL;DR

This paper formulates a Riemann-Hilbert problem for a nonlocal reverse-time six-order AKNS system, deriving soliton solutions and analyzing their dynamics, contributing to the understanding of complex integrable systems.

Contribution

It introduces a novel approach to solving a nonlocal reverse-time six-order AKNS system using Riemann-Hilbert techniques, revealing new soliton solutions and their behaviors.

Findings

Derived explicit soliton solutions for the system

Analyzed the dynamical behaviors of N-solitons

Established a Riemann-Hilbert framework for the system

Abstract

In this paper, we are going to solve nonlinear nonlocal reverse-time six-component six-order AKNS system. We used reverse-time reduction to reduce the coupled system to an integrable six-order NLS-type equation. Starting from the spectral problem of the AKNS system, a Riemann-Hilbert problem will be formulated. This formulation allows to generate soliton solutions by using the vectors lying in the kernel of the matrix Jost solutions. When reflection coefficients are zeros, the jump matrix is identity and the corresponding Riemann-Hilbert problem yields soliton solutions, leading to explore their dynamics.