The Fokas method to the Sasa-Satsuma equation on the half-line

TL;DR

This paper develops a Riemann-Hilbert problem framework for solving the initial-boundary value problem of the Sasa-Satsuma equation on the half-line, providing a new analytical approach for this integrable system.

Contribution

It introduces a Riemann-Hilbert formalism and analyzes the global relation for the Sasa-Satsuma equation on the half-line, advancing the analytical methods for this nonlinear PDE.

Findings

Formulated a Riemann-Hilbert problem for the SS equation

Analyzed the global relation for the initial-boundary value problem

Provides a foundation for solving the SS equation on the half-line

Abstract

We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the Sasa-Satsuma(SS) equation: $iq_T+\frac{1}{2}q_{XX}+|q|^2q+i\eps (q_{XXX}+6|q|^2q_X+3q(|q|^2)_X)=0$ on the half-line. And we also analysis the global relation in this paper.