Leading-order temporal asymptotics of the Fokas-Lenells Equation without solitons

TL;DR

This paper derives the main long-time behavior of solutions to the Fokas-Lenells equation without solitons using the Deift-Zhou method, providing insights into its asymptotic dynamics.

Contribution

It applies the Deift-Zhou method to analyze the leading-order asymptotics of the Fokas-Lenells equation in the absence of solitons, filling a gap in the understanding of its long-time behavior.

Findings

Established the leading-order asymptotics for the solution as time tends to infinity.

Focused on the solitonless sector of the Fokas-Lenells equation.

Provided a rigorous mathematical framework for the asymptotic analysis.

Abstract

We use the Deift-Zhou method to obtain, in the solitonless sector, the leading order asymptotic of the solution to the Cauchy problem of the Fokas-Lenells equation as $t\ra+\infty$ on the full-line.