Integrable and non-integrable equations with peakons

Abstract

We consider a one-parameter family of non-evolutionary partial differential equations which includes the integrable Camassa-Holm equation and a new equation first isolated by Degasperis and Procesi. A Lagrangian and Hamiltonian formulation is presented for the whole family of equations, and we discuss how this fits into a bi-Hamiltonian framework in the integrable cases. The Hamiltonian dynamics of peakons and some other special finite-dimensional reductions are also described.

Proceedings of Nonlinear Physics II: Theory and Experiment, Gallipoli 2002

Cited by in corpus (9)

• A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
• On a Camassa-Holm type equation with two dependent variables
• Dressing Method for the Degasperis-Procesi Equation
• Generalizations of the short pulse equation
• Hamiltonian Structures for the Ostrovsky-Vakhnenko Equation
• A Regularization of Burgers Equation using a Filtered Convective Velocity
• A new integrable structure associated to the Camassa-Holm peakons
• An integrable (2+1)-dimensional Camassa-Holm hierarchy with peakon solutions
• Similarity reductions of peakon equations: the $b$-family