On the Spectral Problem Associated with the Camassa-Holm Equation

DOI10.2991/jnmp.2004.11.4.1zbMath1064.35164OpenAlexW2128370975MaRDI QIDQ4653183

Christer Bennewitz

Publication date: 7 March 2005

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2991/jnmp.2004.11.4.1

zbMATH Keywords

uniquenessbi-Hamiltonian structureshallow water wavesinverse spectral theory for a Sturm-Liouville equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25)

Related Items

Minimization of lowest positive periodic eigenvalue for the Camassa–Holm equation with indefinite potential ⋮ Criterion for Lyapunov stability of periodic Camassa-Holm equations ⋮ Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators ⋮ Poisson structure and action-angle variables for the Camassa-Holm equation ⋮ The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data ⋮ Quadratic operator pencils associated with the conservative Camassa-Holm flow

Cites Work

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• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Spectral Asymptotics for Sturm-Liouville Equations
• The Scattering Approach for the Camassa—Holm equation