# Camassa-Holm cuspons, solitons and their interactions via the dressing method

## TL;DR

This paper applies a dressing method to the Camassa-Holm equation to construct explicit soliton and cuspon solutions, analyze their interactions, and explore geometric aspects via inverse scattering.

## Contribution

It introduces a novel application of the dressing method to generate explicit solutions and study interactions for the Camassa-Holm equation.

## Key findings

- Explicit soliton and cuspon solutions constructed
- Interactions between solitons and cuspons analyzed
- Geometric aspects revisited through inverse scattering

## Abstract

A dressing method is applied to a matrix Lax pair for the Camassa-Holm equation, thereby allowing for the construction of several global solutions of the system. In particular solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa-Holm equation ar re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.