Compact discrete gradient schemes for nonlinear Schrödinger equations
DOI10.1515/ijnsns-2014-0064zbMath1401.65095OpenAlexW2582042605MaRDI QIDQ1662127
Xiuling Yin, Jing-Jing Zhang, Cheng-Jian Zhang
Publication date: 17 August 2018
Published in: International Journal of Nonlinear Sciences and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/ijnsns-2014-0064
KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)
Cites Work
- Unnamed Item
- High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
- Variational iteration method for solving Burgers and coupled Burgers equations
- Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations
- Exp-function method for nonlinear wave equations
- Compact finite difference schemes with spectral-like resolution
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- Variational principles for some nonlinear partial differential equations with variable coefficients
- Homotopy perturbation method for bifurcation of nonlinear problems
- Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term
- Energy-preserving \(H^1\)-Galerkin schemes for shallow water wave equations with peakon solutions
- Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients
- Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
- Construction of solitary solution and compacton-like solution by variational iteration method
- Variational approach for nonlinear oscillators
- A conservative compact finite difference scheme for the KdV equation