A four component cubic peakon (4CH) equations

TL;DR

This paper introduces two novel four-component Camassa-Holm systems with cubic nonlinearity, detailing their Lax pairs and Hamiltonian structures, and relating them to existing three- and two-component models.

Contribution

The paper presents two new four-component cubic Camassa-Holm systems, expanding the class of integrable models with explicit Lax pairs and Hamiltonian structures.

Findings

First system generalizes the 3CH system by Xia, Zhou, and Qiao.

Second system extends the Novikov system to four components.

Both systems possess integrable structures such as Lax pairs and Hamiltonians.

Abstract

Two different four component Camassa-Holm (4CH) systems with cubic nonlinearity are proposed. The Lax pair and Hamiltonian structure are defined for both (CH) systems. The first (4CH) system include as a special case the (3CH) system considered by Xia, Zhou and Qiao, while the second contains the two-component generalization of Novikov system considered by Geng and Xiu.