Invariants-preserving integration of the modified Camassa-Holm equation

DOI10.1007/s13160-011-0043-zzbMath1231.65144OpenAlexW2144415748MaRDI QIDQ645281

Yuto Miyatake, Daisuke Furihata, Takayasu Matsuo

Publication date: 14 November 2011

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-011-0043-z

zbMATH Keywords

conservation lawsnumerical examplesbi-Hamiltonian structureshallow water wavesmodified Camassa-Holm equationcompletely integrablesoliton equationdiscrete variational derivative method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Soliton equations (35Q51)

Related Items (4)

Energy-preserving \(H^1\)-Galerkin schemes for shallow water wave equations with peakon solutions ⋮ Numerical integration of the Ostrovsky equation based on its geometric structures ⋮ The effect of a noise on the stochastic modified Camassa–Holm equation ⋮ A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation

Cites Work

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• Conservative finite difference schemes for the modified Camassa-Holm equation
• Discrete Variational Derivative Method
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