Stability for the periodic Camassa-Holm equation

2005/12/01 by Jonatan Lenells · 33 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Camassa–Holm equation #Mathematics #Stability (learning theory) #Mathematical analysis #Periodic wave #Traveling wave #Integrable system #Computer science

paper · pdf · doi:10.7146/math.scand.a-14971

published in MATHEMATICA SCANDINAVICA 97(2), 188 (Aarhus University Library)

openalex publication_date 2005/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

We use integrability to prove the stability of smooth periodic solutions of the Camassa-Holm equation. In particular, the smooth periodic traveling wave solutions are shown to be orbitally stable.

Citations

• A New Integrable Shallow Water Equation
• On the Inverse Spectral Problem for the Camassa–Holm Equation
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Global Weak Solutions for a Shallow Water Equation
• On the Cauchy problem for the Camassa–Holm equation
• Traveling wave solutions of the Camassa–Holm equation
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• The correspondence between KdV and Camassa-Holm
• 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
• Conservation laws of the Camassa–Holm 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
• A Variational Approach to the Stability of Periodic Peakons

Cited by

• Camassa–Holm equation [wikipedia]