A synthetical two-component model with peakon solutions

TL;DR

This paper introduces a generalized two-component model with peakon solutions, encompassing existing integrable equations, and explores its mathematical properties, including Lax pairs, conservation laws, and novel peakon interactions.

Contribution

It presents a new generalized two-component system with peakon solutions, including a novel non-traveling wave type of N-peakon solutions, expanding the understanding of integrable peakon equations.

Findings

The model admits Lax pairs and infinite conservation laws.

It includes existing integrable peakon equations as special cases.

A new non-traveling N-peakon solution is derived.

Abstract

A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized two-component system is shown to possess Lax pair and infinitely many conservation laws. Bi-Hamiltonian structures and peakon interactions are discussed in detail for typical representative equations of the generalized system. In particular, a new type of $N$-peakon solution, which is not in the traveling wave type, is obtained from the generalized system.