Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrödinger equations

DOI10.1016/j.apnum.2010.10.008zbMath1207.65120OpenAlexW1996369475MaRDI QIDQ624978

Huayu Hu, Yaming Chen, Huajun Zhu, Songhe Song

Publication date: 11 February 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.10.008

zbMATH Keywords

Hamiltoniannumerical experimentsautocorrelation functionwavelet collocation methodsymplecticmulti-symplectictwo-dimensional Schrödinger equationDaubechies scaling functions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Numerical methods for wavelets (65T60) NLS equations (nonlinear Schrödinger equations) (35Q55) 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

A meshless scheme for Hamiltonian partial differential equations with conservation properties ⋮ Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations ⋮ Multi-symplectic quasi-interpolation method for the KdV equation ⋮ Meshless symplectic and multi-symplectic local RBF collocation methods for nonlinear Schrödinger equation ⋮ Multiple-soliton solutions and a generalized double Wronskian determinant to the \((2+1)\)-dimensional nonlinear Schrödinger equations ⋮ Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations ⋮ A meshless symplectic method for two-dimensional nonlinear Schrödinger equations based on radial basis function approximation ⋮ Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation ⋮ The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs ⋮ Multi-symplectic quasi-interpolation method for Hamiltonian partial differential equations ⋮ A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method ⋮ A space-time fully decoupled wavelet Galerkin method for solving multidimensional nonlinear Schrödinger equations with damping ⋮ Computing a numerical solution of two dimensional non-linear Schrödinger equation on complexly shaped domains by RBF based differential quadrature method ⋮ An energy-momentum conserving scheme for Hamiltonian wave equation based on multiquadric trigonometric quasi-interpolation ⋮ The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory

Cites Work

• Unnamed Item
• Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation
• The multisymplectic numerical method for Gross-Pitaevskii equation
• Splitting multisymplectic integrators for Maxwell's equations
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• A fast adaptive wavelet collocation algorithm for multidimensional PDEs
• Numerical methods for the simulation of trapped nonlinear Schrödinger systems
• Multisymplectic box schemes and the Korteweg-de Vries equation.
• Local discontinuous Galerkin methods for nonlinear Schrödinger equations
• A numerical scheme for the simulation of blow-up in the nonlinear Schrödinger equation
• A wavelet collocation method for the numerical solution of partial differential equations
• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• Symplectic wavelet collocation method for Hamiltonian wave equations
• Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
• Numerical simulation of singular solutions to the two-dimensional cubic schrödinger equation
• Splitting methods
• Multi-symplectic Spectral Methods for the Sine-Gordon Equation
• On the multisymplecticity of partitioned Runge–Kutta and splitting methods
• On the Representation of Operators in Bases of Compactly Supported Wavelets
• Multi-symplectic structures and wave propagation
• Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation
• Multisymplectic geometry and multisymplectic Preissman scheme for the KP equation
• Conservation of wave action under multisymplectic discretizations
• Linear PDEs and Numerical Methods That Preserve a Multisymplectic Conservation Law
• On the Construction and Comparison of Difference Schemes
• Symplectic methods for the nonlinear Schrödinger equation
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
• Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation