Conservative finite difference schemes for the generalized Zakharov-Kuznetsov equations

DOI10.1016/j.cam.2011.04.010zbMath1237.65096OpenAlexW2011204662MaRDI QIDQ415218

Shinnosuke Oharu, Takahiro Noi, Hirota Nishiyama

Publication date: 11 May 2012

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.2011.04.010

zbMATH Keywords

discrete variational methodconservative finite difference schemedivision and collision of nonlinear wavesgeneralized Zakharov-Kuznetsov equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (3)

Structure-preserving reduced-order modeling of Korteweg-de Vries equation ⋮ A conservative fourth-order stable finite difference scheme for the generalized Rosenau-KdV equation in both 1D and 2D ⋮ Linearly Implicit Local and Global Energy-Preserving Methods for PDEs with a Cubic Hamiltonian

Cites Work

• On the energetic Galerkin boundary element method applied to interior wave propagation problems
• Cylindrical quasi-solitons of the Zakharov-Kuznetsov equation
• Some relatively new techniques for nonlinear problems
• Two-dimensional amplitude evolution equations for nonlinear dispersive waves on thin films
• High-order nonreflecting boundary conditions for the dispersive shallow water equations.
• High-order difference methods for waves in discontinuous media
• On finite-difference methods for the Korteweg-de Vries equation
• Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equa\-tions
• On Stability of Some Finite Difference Schemes for the Korteweg-de Vries Equation
• A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations
• Nonlinear ion-acoustic waves in weak magnetic fields
• A numerical and theoretical study of certain nonlinear wave phenomena
• Pseudo-spectral/finite-difference adaptive method for spherical shallow-water equations

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