Solitons in the Camassa-Holm shallow water equation

1993/11/22 by Fred Cooper, Harvey Shepard, Harvey K. Shepard · 81 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Amplitude #Camassa–Holm equation #Class (philosophy) #Derivative (finance) #Geometry #Integrable system #Lagrangian #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Scaling #Shallow water equations #Soliton #Thermodynamics #Variable (mathematics) #Waves and shallow water #nlin.PS #patt-sol

paper · pdf · doi:10.1016/0375-9601(94)91246-7

published in Physics Letters A 194(4), 246-250 (Elsevier BV) · 8 pages, LaTex, no figures

arxiv created 1993/11/22 · openalex publication_date 1994/11/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the class of shallow water equations of Camassa and Holm derived from the Lagrangian: L= ∫ ( (1)/(2) (φ_xxx-φ_x )φ_t - 1 \over 2 (φ_x)³ - 1 \over 2φ_x(φ_xx)² - 1 \over 2 κφ_x² ) dx,

Citations

• Variational method for studying solitons in the Korteweg-de Vries equation
• Post-Gaussian variational method for the nonlinear Schrödinger equation: Soliton behavior and blowup

Cited by

• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation