Riemann-Hilbert problem of the three-component coupled Sasa-Satsuma equation and its multi-soliton solutions

TL;DR

This paper applies the Riemann-Hilbert method to analyze the inverse scattering transform of the three-component coupled Sasa-Satsuma equation, deriving multi-soliton solutions and exploring their dynamics.

Contribution

It introduces a novel spectral analysis approach for a 7x7 Lax pair and constructs explicit multi-soliton solutions for the coupled equation.

Findings

Derived N-soliton solutions for the equation.

Analyzed soliton dynamics with graphical illustrations.

Formulated a Riemann-Hilbert problem for the spectral analysis.

Abstract

In this work, the inverse scattering transform of the three-component coupled Sasa-Satsuma equation is investigated via the Riemann-Hilbert method. Firstly we consider a Lax pair associated with a $7\times 7$ matrix spectral problem for the equation. Then we present the spectral analysis of the Lax pair, from which a kind of Riemann-Hilbert problem is formulated. Moreover, $N$-soliton solutions to the equation are constructed through a particular Riemann-Hilbert problem with vanishing scattering coefficients. Finally, the dynamics of the soliton solutions are discussed with some graphics.