Finite propagation speed for the Camassa–Holm equation

2005/02/01 by Adrian Constantin · 146 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Applied mathematics #Camassa–Holm equation #Integrable system #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Partial differential equation #Physics

paper · doi:10.1063/1.1845603

published in Journal of Mathematical Physics 46(2) (American Institute of Physics)

openalex publication_date 2005/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

We prove that any classical solution of the Camassa–Holm equation will have compact support if its initial data has this property.

Citations

• On the Inverse Spectral Problem for the Camassa–Holm Equation
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Global Weak Solutions for a Shallow Water Equation
• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Wave breaking for nonlinear nonlocal shallow water equations
• Geodesic flow on the diffeomorphism group of the circle
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation

Cited by

• Evolution of the Scattering Coefficients of the Camassa–Holm Equation, for General Initial Data
• Camassa–Holm equation [wikipedia]