Global conservative solutions of the Camassa-Holm equation for initial data nonvanishing asymptotics

TL;DR

This paper investigates global conservative solutions to the Camassa-Holm equation with initial data that does not vanish at infinity, focusing on solutions that preserve energy and structure over time.

Contribution

It introduces a framework for analyzing solutions with nonvanishing asymptotics, extending previous results to more general initial conditions.

Findings

Established existence of global conservative solutions for nonvanishing asymptotics

Extended the theory of Camassa-Holm solutions to broader initial data classes

Provided insights into the long-term behavior of solutions with non-zero limits at infinity

Abstract

We study global conservative solutions of the Cauchy problem for the Camassa-Holm equation $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with nonvanishing and distinct spatial asymptotics.