Soliton asymptotics for the KdV shock problem of low regularity

TL;DR

This paper improves the understanding of the long-term behavior of solutions to the KdV shock problem at low regularity by extending asymptotic formulas using Riemann-Hilbert analysis.

Contribution

It introduces a new approach that broadens the applicability of asymptotic formulas for the KdV shock problem with less restrictive initial data conditions.

Findings

Extended the domain of validity for asymptotic formulas.

Reduced decay and smoothness requirements for initial data.

Enhanced the analytical framework for low-regularity KdV solutions.

Abstract

We revisit the asymptotic analysis of the KdV shock problem in the soliton region. Our approach is based on the analysis of the associated Riemann-Hilbert problem and we extend the domain of validity of the asymptotic formulas while at the same time requiring less decay and smoothness for the initial data.