Complete integrable particle methods and the recurrence of initial states for a nonlinear shallow-water wave equation

DOI10.1016/j.jcp.2008.04.011zbMath1201.76029OpenAlexW2170576189MaRDI QIDQ934118

Roberto Camassa, Long Lee

Publication date: 29 July 2008

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2008.04.011

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Particle methods and lattice-gas methods (76M28)

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Cites Work

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• A convergent numerical scheme for the Camassa-Holm equation based on multipeakons
• The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
• Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation
• Characteristics and the initial value problem of a completely integrable shallow water equation
• Integral and integrable algorithms for a nonlinear shallow-water wave equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Fourier Methods with Extended Stability Intervals for the Korteweg–de Vries Equation
• A continuum limit of the Toda lattice
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• On a Completely Integrable Numerical Scheme for a Nonlinear Shallow-Water Wave Equation