# Existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation

## TL;DR

This paper proves the existence and uniqueness of global weak solutions for a generalized Camassa-Holm equation by transforming it into semi-linear systems and analyzing their solutions.

## Contribution

It introduces a novel transformation of the equation into semi-linear systems to establish solution existence and uniqueness.

## Key findings

- Global weak solutions exist and are unique.
- Transformation into semi-linear systems is effective.
- Results apply to the real line setting.

## Abstract

This paper is concerned with the existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation on real line. By introducing some new variables, the equation is transformed into two different semi-linear systems. Then the existence and uniqueness of global weak solutions to the original equation are obtained from that of the two semi-linear systems, respectively.