GLOBAL CONSERVATIVE MULTIPEAKON SOLUTIONS OF THE CAMASSA–HOLM EQUATION

2007/03/01 by Helge Holden, Xavier Raynaud · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Algebraic structures and combinatorial models #Construct (python library) #Peakon #Camassa–Holm equation #Ordinary differential equation #Mathematics #Set (abstract data type) #Constant (computer programming) #Applied mathematics #Mathematical analysis #Differential equation #Computer science #Integrable system

paper · doi:10.1142/s0219891607001045

openalex publication_date 2007/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how to construct globally defined multipeakon solutions of the Camassa–Holm equation. The construction includes in particular the case with peakon-antipeakon collisions. The solutions are conservative in the sense that the associated energy is constant for almost all times. Furthermore, we construct a new set of ordinary differential equations that determines the multipeakons globally. The system remains globally well-defined.

Citations

• A New Integrable Shallow Water Equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Global Conservative Solutions of the Camassa–Holm Equation
• Global Weak Solutions for a Shallow Water Equation
• A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General H¹ Initial Data
• On the scattering problem for the Camassa-Holm equation
• Integral and integrable algorithms for a nonlinear shallow-water wave equation
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• Orbital stability of solitary waves for a shallow water equation
• Wave breaking for nonlinear nonlocal shallow water equations
• Convergence of a Finite Difference Scheme for the Camassa–Holm Equation
• Multipeakons and the Classical Moment Problem

Cited by

• Periodic conservative solutions of the Camassa–Holm equation
• Camassa–Holm equation [wikipedia]