Long-time asymptotics for the Hirota equation on the half-line

TL;DR

This paper analyzes the long-time behavior of solutions to the Hirota equation on the half-line using Riemann-Hilbert problem techniques, providing insights into its asymptotic properties.

Contribution

It introduces a method to study the long-time asymptotics of the Hirota equation on the half-line via matrix Riemann-Hilbert problem analysis.

Findings

Characterization of long-time asymptotics for the Hirota equation

Application of Riemann-Hilbert problem techniques to boundary value problems

Insights into the decay and oscillation behavior of solutions

Abstract

We consider the Hirota equation on the quarter plane with the initial and boundary values belonging to the Schwartz space. The goal of this paper is to study the long-time behavior of the solution of this initial-boundary value problem based on the asymptotic analysis of an associated matrix Riemann--Hilbert problem.