The parametrix problem for Toda equation with steplike initial data

TL;DR

This paper rigorously solves the parametrix problem for the Toda equation with steplike initial data, providing a complete asymptotic analysis that confirms previous results and advances understanding of the Toda rarefaction problem.

Contribution

It offers the first rigorous solution to the parametrix problem for the Toda rarefaction problem with steplike initial data and completes its asymptotic analysis.

Findings

Rigorous solution of the parametrix problem for Toda rarefaction.

Complete asymptotic analysis confirming previous results.

Justification of asymptotics from prior work.

Abstract

This paper is a continuation of arXiv:17.01.02867. We give here rigorous solution of the parametrix problem for Toda rarefaction problem and complete asymptotic analysis, justifying the asymptotics obtained in arXiv:17.01.02867.