Efficient mass- and energy-preserving schemes for the coupled nonlinear Schrödinger-Boussinesq system

DOI10.1016/j.aml.2018.11.024zbMath1435.65171OpenAlexW2902201739MaRDI QIDQ1726636

Bin Yang, Chun Zhang, Jiaxiang Cai

Publication date: 20 February 2019

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

Full work available at URL: https://doi.org/10.1016/j.aml.2018.11.024

zbMATH Keywords

fast Fourier transformHamiltonian systemSchrödinger-Boussinesq equationdiscrete gradient method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for discrete and fast Fourier transforms (65T50) 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) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations, Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations, A dissipation-preserving finite-difference scheme for a generalized Higgs boson equation in the de Sitter space-time, Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled <scp>Schrödinger–Boussinesq</scp> equations, Two energy-preserving Fourier pseudo-spectral methods and error estimate for the Klein-Gordon-Dirac system, Efficient eighth‐order accurate energy‐preserving compact difference schemes for the coupled Schrödinger–Boussinesq equations, Fully-decoupled conservative exponential approaches for the coupled nonlinear Schrödinger-Boussinesq equations, Structure-preserving BDF2 FE method for the coupled Schrödinger-Boussinesq equations, Efficient energy-preserving wavelet collocation schemes for the coupled nonlinear Schrödinger-Boussinesq system, A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schrödinger-Boussinesq (SBq) equations, A mass and energy conservative fourth-order compact difference scheme for the Klein-Gordon-Dirac \(\text{equations}^{\star}\)

Cites Work

• Unnamed Item
• Unnamed Item
• The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods
• Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations
• The time-splitting Fourier spectral method for the coupled Schrödinger-Boussinesq equations
• A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation
• A general framework for finding energy dissipative/conservative \(H^1\)-Galerkin schemes and their underlying \(H^1\)-weak forms for nonlinear evolution equations
• Hamiltonian-conserving discrete canonical equations based on variational difference quotients
• Exact explicit solutions of the nonlinear Schrödinger equation coupled to the Boussinesq equation
• Time-splitting combined with exponential wave integrator Fourier pseudospectral method for Schrödinger-Boussinesq system
• Decoupled local/global energy-preserving schemes for the \(N\)-coupled nonlinear Schrödinger equations
• Numerical analysis of cubic orthogonal spline collocation methods for the coupled Schrödinger-Boussinesq equations
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Two Energy-Conserved Splitting Methods for Three-Dimensional Time-Domain Maxwell's Equations and the Convergence Analysis
• A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
• Conservative compact finite difference scheme for the coupled <scp>S</scp>chrödinger–<scp>B</scp>oussinesq equation
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs