Long-time asymptotics for initial-boundary value problems of integrable Fokas-Lenells equation on the half-line

TL;DR

This paper analyzes the long-time behavior of solutions to the integrable Fokas-Lenells equation on the half-line using Riemann-Hilbert problem techniques, providing asymptotic descriptions for initial-boundary value problems.

Contribution

It applies the Deift-Zhou nonlinear steepest descent method to derive long-time asymptotics for IBV problems of the Fokas-Lenells equation on the half-line, advancing understanding of its integrable dynamics.

Findings

Asymptotic formulas for solutions as t→∞

Characterization of boundary effects on long-time behavior

Extension of Riemann-Hilbert analysis to IBV problems

Abstract

We study the Schwartz class of initial-boundary value (IBV) problems for the integrable Fokas-Lenells equation on the half-line via the Deift-Zhou's nonlinear descent method analysis of the corresponding Riemann-Hilbert problem such that the asymptotics of the Schwartz class of IBV problems as t\to\infty is presented.