The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs

DOI10.1016/j.cam.2011.08.023zbMath1231.65173OpenAlexW2086306198MaRDI QIDQ654745

Songhe Song, Yaming Chen, Huajun Zhu

Publication date: 21 December 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.08.023

zbMATH Keywords

conservation lawsnumerical examplesHamiltonian PDEsemidiscretizationKP equationKadomtsev-Petviashvili equationZakharov-Kuznetsov equationZK equationmulti-symplectic Fourier pseudospectral method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (10)

Structure-preserving reduced-order modeling of Korteweg-de Vries equation ⋮ Global energy preserving model reduction for multi-symplectic PDEs ⋮ A meshless symplectic method for two-dimensional nonlinear Schrödinger equations based on radial basis function approximation ⋮ Serre-type Equations in Deep Water ⋮ A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation ⋮ On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties ⋮ Linearly Implicit Local and Global Energy-Preserving Methods for PDEs with a Cubic Hamiltonian ⋮ A Splitting Method for the Degasperis--Procesi Equation Using an Optimized WENO Scheme and the Fourier Pseudospectral Method ⋮ A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions ⋮ Optimal error estimate of a linear Fourier pseudo-spectral scheme for two dimensional Klein-Gordon-Schrödinger equations

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