Long-time asymptotics for the Sasa-Satsuma equation via nonlinear steepest descent method

TL;DR

This paper develops a Riemann-Hilbert problem framework and applies nonlinear steepest descent to analyze the long-time behavior of solutions to the Sasa-Satsuma equation, a nonlinear wave equation.

Contribution

It introduces a $3\times3$ Riemann-Hilbert problem formulation and uses nonlinear steepest descent to derive long-time asymptotics for the Sasa-Satsuma equation.

Findings

Representation of solutions via Riemann-Hilbert problem

Asymptotic formulas for long-time behavior

Method applicable to integrable nonlinear equations

Abstract

We formulate a $3\times3$ Riemann-Hilbert problem to solve the Cauchy problem for the Sasa-Satsuma equation on the line, which allows us to give a representation for the solution of Sasa-Satsuma equation. We then apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Sasa-Satsuma equation.