Long time behaviour for a class of low-regularity solutions of the Camassa-Holm equation

TL;DR

This paper studies the long-term dynamics of low-regularity solutions to the Camassa-Holm equation, focusing on solutions composed of infinitely many interacting traveling waves with peaked corners.

Contribution

It introduces a new analysis of low-regularity solutions involving infinite superpositions of peaked traveling waves, advancing understanding of their long-time behavior.

Findings

Characterization of long-time behavior of superposed peaked waves

Insights into stability and interaction of low-regularity solutions

Extension of previous results to infinite wave superpositions

Abstract

In this paper, we investigate the long time behaviour for a class of low-regularity solutions of the Camassa-Holm equation given by the superposition of infinitely many interacting traveling waves with corners at their peaks.