# Weakly integrable Camassa-Holm-type equations

## TL;DR

This paper constructs a series of deformed Camassa-Holm-type equations using advanced algebraic methods, demonstrating their weak integrability through modified Lax pairs, contributing to the understanding of integrable systems.

## Contribution

It introduces new weakly integrable Camassa-Holm-type equations via Lagrangian deformation and Loop algebra splittings, expanding the class of known integrable models.

## Key findings

- Equations are weakly integrable with modified Lax pairs
- New algebraic methods applied to deform classical equations
- Enhances understanding of integrability in nonlinear wave equations

## Abstract

Series of deformed Camassa-Holm-type equations are constructed using the Lagrangian deformation and Loop algebra splittings. They are weakly integrable in the sense of modified Lax pairs.