On the scattering problem for the Camassa-Holm equation

2001/04/08 by Adrian Constantin · 694 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Advanced Mathematical Physics Problems #Camassa–Holm equation #Eigenvalues and eigenvectors #Scattering #Mathematical analysis #Mathematics #Motion (physics) #Physics #Mathematical physics #Classical mechanics #Optics #Quantum mechanics #Integrable system

paper · doi:10.1098/rspa.2000.0701

published in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 457(2008), 953-970 (Royal Society)

openalex publication_date 2001/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

The Camassa–Holm equation has a number of constants of motion arising as eigenvalues of an associated spectral problem. We give a description of the spectral picture and discuss the scattering problem.

Citations

• A New Integrable Shallow Water Equation
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Inverse scattering on the line

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• The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations
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• Camassa–Holm equation [wikipedia]