Symplectic structure-preserving integrators for the two-dimensional Gross-Pitaevskii equation for BEC

DOI10.1016/j.cam.2011.04.019zbMath1223.65097OpenAlexW2158531219MaRDI QIDQ633948

Jing Chen, Jialin Hong, Linghua Kong, Fangfang Fu

Publication date: 2 August 2011

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.2011.04.019

zbMATH Keywords

numerical resultsconservation lawsGross-Pitaevskii equationerror estimationsBose-Einstein condensatesymplectic integratorsplitting symplectic integrator

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (10)

Multisymplectic structure-preserving scheme for the coupled Gross–Pitaevskii equations ⋮ Numerical Solution of Shrödinger Equations Based on the Meshless Methods ⋮ General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs ⋮ Symplectic‐preserving Fourier spectral scheme for space fractional<scp>Klein–Gordon–Schrödinger</scp>equations ⋮ Finding multiple solutions to elliptic systems with polynomial nonlinearity ⋮ Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs ⋮ Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model ⋮ A Galerkin Splitting Symplectic Method for the Two Dimensional Nonlinear Schrödinger Equation ⋮ An energy-preserving Crank-Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrödinger equation ⋮ Lattice Boltzmann model for the interaction of \((2+1)\)-dimensional solitons in generalized Gross-Pitaevskii equation

Cites Work

• Unnamed Item
• The multisymplectic numerical method for Gross-Pitaevskii equation
• Generating functions of multi-symplectic RK methods via DW Hamilton-Jacobi equations
• Splitting multisymplectic integrators for Maxwell's equations
• Numerical methods for the simulation of trapped nonlinear Schrödinger systems
• Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation
• Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term
• Quadratic invariants and multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
• Conserved quantities of some Hamiltonian wave equations after full discretization
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• Splitting methods
• Symplectic integration of Hamiltonian systems
• Multi-symplectic Spectral Methods for the Sine-Gordon Equation
• COMPARISON OF FINITE‐DIFFERENCE SCHEMES FOR THE GROSS‐PITAEVSKII EQUATION
• Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation
• HAMILTONIAN INTEGRATORS FOR THE NONLINEAR SCHROEDINGER EQUATION
• Symplectic Euler Method for Nonlinear High Order Schrödinger Equation with a Trapped Term
• Novel Multi-symplectic Integrators for Nonlinear Fourth-order Schrödinger Equation with Trapped Term
• Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation
• On the Construction and Comparison of Difference Schemes

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