Multi-symplectic Runge-Kutta-Nyström methods for nonsmooth nonlinear Schrödinger equations

DOI10.1016/j.jmaa.2016.06.060zbMath1345.65065OpenAlexW2464216191MaRDI QIDQ530355

Jiejing Bai

Publication date: 29 July 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.06.060

zbMATH Keywords

conservation lawsnumerical experimentnonlinear Schrödinger equationsdelta potentialsmulti-symplectic Runge-Kutta-Nyström methodsweak multi-symplectic Hamiltonian systems

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) NLS equations (nonlinear Schrödinger equations) (35Q55) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Existence and uniqueness of time periodic solutions for quantum versions of three-dimensional Schrödinger equations ⋮ Energy-preserving methods for non-smooth nonlinear Schrödinger equations ⋮ Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Uses Software

• IIMPACK

Cites Work

• Unnamed Item
• Unnamed Item
• On the preservation of phase space structure under multisymplectic discretization
• Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• EJIIM for the stationary Schrödinger equations with delta potential wells
• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients
• Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
• High Order Multisymplectic Runge--Kutta Methods
• Simulating Hamiltonian Dynamics
• The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems
• Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
• Multi-symplectic structures and wave propagation
• Bound and resonance states of the nonlinear Schrödinger equation in simple model systems
• Numerical methods for Hamiltonian PDEs
• The Immersed Interface Method
• Geometric integrators for the nonlinear Schrödinger equation