Derivation of the multisymplectic Crank-Nicolson scheme for the nonlinear Schrödinger equation

DOI10.1016/j.cpc.2014.05.011zbMath1360.35237OpenAlexW2058938801MaRDI QIDQ525839

Wenjun Cai, Yong-Zhong Song, Yu Shun Wang

Publication date: 5 May 2017

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2014.05.011

zbMATH Keywords

conservation lawnonlinear Schrödinger equationCrank-Nicolson schemevariational integratormultisymplectic integrator

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

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Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system

Cites Work

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• Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation
• Concatenating construction of the multisymplectic schemes for \(2+1\)-dimensional sine-Gordon equation
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Symplectic integration of Hamiltonian wave equations
• Symplectic integrators for the Ablowitz-Ladik discrete nonlinear Schrödinger equation
• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation
• A multisymplectic variational integrator for the nonlinear Schrödinger equation
• On Multisymplecticity of Partitioned Runge–Kutta Methods
• An Alternating Crank--Nicolson Method for Decoupling the Ginzburg--Landau Equations
• Multi-symplectic structures and wave propagation
• Novel Multi-symplectic Integrators for Nonlinear Fourth-order Schrödinger Equation with Trapped Term
• Numerical methods for Hamiltonian PDEs
• Symplectic methods for the nonlinear Schrödinger equation
• Symplectic methods for the nonlinear Schrödinger equation
• A variational approach to second-order multisymplectic field theory
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
• Geometric integrators for the nonlinear Schrödinger equation

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