A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions

TL;DR

This paper introduces a generalized nonisospectral Camassa-Holm equation that admits multipeakon solutions, utilizing determinant techniques and establishing a nonisospectral Lax pair, expanding the understanding of integrable shallow water wave models.

Contribution

It presents a new generalized Camassa-Holm equation with multipeakon solutions and a nonisospectral Lax pair, extending prior models with a novel determinant-based approach.

Findings

The new equation admits multipeakon solutions.

It possesses a nonisospectral Lax pair.

The approach is based on classic determinant techniques.

Abstract

Motivated by the paper (Beals, Sattinger and Szmigielski, Adv. Math. 154 (2000) 229--257), we propose an extension of the Camassa-Holm equation, which also admits the multipeakon solutions. The novel aspect is that our approach is mainly based on classic determinant technique. Furthermore, the proposed equation is shown to possess a nonisospectral Lax pair.