Multisymplectic geometry, local conservation laws and Fourier pseudospectral discretization for the ``good Boussinesq equation

DOI10.1016/j.amc.2003.12.009zbMath1065.65140OpenAlexW2037327929MaRDI QIDQ1763219

Jing-Bo Chen

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.12.009

zbMATH Keywords

Boussinesq equationConservation lawsFourier pseudospectral discretizationMultisymplectic Lagrangian and Hamiltonian formulation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Derivation of Lagrangian density for the ``good Boussinesq equation and multisymplectic disretizations ⋮ A meshless multi-symplectic local radial basis function collocation scheme for the ``good Boussinesq equation ⋮ New conservative schemes with discrete variational derivatives for nonlinear wave equations ⋮ Fractional theoretical model for gravity waves and squall line in complex atmospheric motion ⋮ On the Elliptic-Hyperbolic Transition in Whitham Modulation Theory ⋮ Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs ⋮ Exact combined traveling wave solutions and multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equations ⋮ Numerical simulation of interaction between Schrödinger field and Klein-Gordon field by multisymplectic method ⋮ Numerical studies on Boussinesq-type equations via a split-step Fourier method ⋮ Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory ⋮ Symplectic and multisymplectic Lobatto methods for the “good” Boussinesq equation

Cites Work

• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Nonlinear stability and convergence of finite-difference methods for the good Boussinesq equation
• Numerical Solutions of the Good Boussinesq Equation
• Soliton and antisoliton interactions in the ‘‘good’’ Boussinesq equation
• Pseudospectral Method for the "Good" Boussinesq Equation
• A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities
• Multi-symplectic structures and wave propagation
• A Practical Guide to Pseudospectral Methods
• Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
• Unnamed Item
• Unnamed Item
• Unnamed Item