An integrable (2+1)-dimensional Camassa-Holm hierarchy with peakon solutions

TL;DR

This paper introduces a new (2+1)-dimensional generalized Camassa-Holm hierarchy featuring both quadratic and cubic nonlinearities, along with its Lax representation and peakon solutions, expanding understanding of integrable systems.

Contribution

It presents a novel (2+1)-dimensional integrable hierarchy with explicit peakon solutions and a Lax pair, enhancing the study of nonlinear wave equations.

Findings

Derived the Lax representation for the 2dgCH system.

Constructed explicit peakon solutions.

Established integrability of the new hierarchy.

Abstract

In this letter, we propose a (2+1)-dimensional generalized Camassa-Holm (2dgCH) hierarchy with both quadratic and cubic nonlinearity. The Lax representation and peakon solutions for the 2dgCH system are derived.