A synthetical two-component model with peakon solutions

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.

to appear in Studies in Applied Mathematics

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• A new two-component integrable system with peakon solutions
• A four-component Camassa-Holm type hierarchy
• Stability of stationary solutions for nonintegrable peakon equations

Cited by in corpus (7)

• Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation
• Alice-Bob Peakon Systems
• Two-component generalizations of the Camassa-Holm equation
• A view of the peakon world through the lens of approximation theory
• Reciprocal link for a coupled Camassa-Holm type equation
• On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system
• On the well-posedness of the Cauchy problem for the two-component peakon system in $C^k\cap W^{k,1}$