Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation

DOI10.1007/s10409-012-0070-2zbMath1345.35089OpenAlexW2037040994MaRDI QIDQ315222

Wen-Rong Zhang, Zi-Chen Deng, Yu-Yue Qin, Wei-Peng Hu

Publication date: 19 September 2016

Published in: Acta Mechanica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10409-012-0070-2

zbMATH Keywords

conservation lawJacobi elliptic functionperiodic wave solutionmulti-symplecticgeneralized \((2+1)\)-dimensional KdV-mKdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (4)

A quartic trigonometric tension B‐spline finite element method for solving Gardner equation ⋮ Highly accurate symplectic element based on two variational principles ⋮ Lie symmetry, nonlocal symmetry analysis, and interaction of solutions of a \((2+1)\)-dimensional KdV-mKdV equation ⋮ Exact solutions and multi-symplectic structure of the generalized KdV-type equation

Cites Work

• Exotic interactions between solitons of the \((2+1)\)-dimensional KdV equation
• An improved generalized \(F\)-expansion method and its application to the \((2 + 1)\)-dimensional KdV equations
• Numerical simulation of KdV and mKdv equations with initial conditions by the variational iteration method
• Exact periodic and solitary waves and their interactions for the \((2+1)\)-dimensional KdV equation
• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms
• Exotic localized structures based on variable separation solution of \((2+1)\)-dimensional KdV equation via the extended tanh-function method
• New exact travelling waves solutions to the combined KdV-MKdV and generalized Zakharov equations
• Multi-symplectic Spectral Methods for the Sine-Gordon Equation
• The Painlevé property for partial differential equations
• Multi-symplectic structures and wave propagation
• Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

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