Traveling wave solutions of the Camassa–Holm equation

2004/11/16 by Jonatan Lenells · 287 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Camassa–Holm equation #Gravitational singularity #Integrable system #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Traveling wave

paper · doi:10.1016/j.jde.2004.09.007

published in Journal of Differential Equations 217(2), 393-430 (Elsevier BV)

openalex publication_date 2004/11/16 · crossref created 2004/11/16 · crossref issued 2005/10/01 · crossref published 2005/10/01 · crossref published-print 2005/10/01 · crossref deposited 2023/04/30 · openalex created_date 2025/10/10 · crossref indexed 2026/08/07 · openalex updated_date 2026/08/08

Citations

• A New Integrable Shallow Water Equation
• On the Inverse Spectral Problem for the Camassa–Holm Equation
• The Camassa–Holm equation for water waves moving over a shear flow
• 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
• The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
• On the blow-up rate and the blow-up set of breaking waves 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
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Orbital stability of solitary waves for a shallow water equation
• Wave breaking for nonlinear nonlocal shallow water equations
• Geodesic flow on the diffeomorphism group of the circle
• Stability of the Camassa-Holm solitons
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• On the Blow-Up of Solutions of a Periodic Shallow Water Equation

Cited by

• Infinite propagation speed of the Camassa–Holm equation
• Conservation laws of the Camassa–Holm equation
• Stability for the periodic Camassa-Holm equation
• Camassa–Holm equation [wikipedia]