A Variational Approach to the Stability of Periodic Peakons

2004/01/01 by Jonatan Lenells · 2 citations
Physics and Astronomy · Mathematics · Earth and Planetary Sciences · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Ocean Waves and Remote Sensing #Mathematics #Stability (learning theory) #Mathematical analysis #Applied mathematics #Computer science

paper · pdf · doi:10.2991/jnmp.2004.11.2.2

openalex publication_date 2004/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The peakons are peaked traveling wave solutions of an integrable shallow water equation. We present a variational proof of their stability.

Citations

• 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
• On the Cauchy problem for the Camassa–Holm equation
• 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
• Wave breaking for nonlinear nonlocal shallow water equations

Cited by

• Stability for the periodic Camassa-Holm equation
• Camassa–Holm equation [wikipedia]