Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation

DOI10.4208/aamm.2015.m1356zbMath1488.65518OpenAlexW2577637577MaRDI QIDQ5155262

Mingzhan Song, Songhe Song, Hong Zhang, Xu Qian

Publication date: 6 October 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.2015.m1356

zbMATH Keywords

nonlinear Schrödinger equationKorteweg-de Vries equationHamiltonian-preservingHamiltonian boundary value method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Time-dependent Schrödinger equations and Dirac equations (35Q41) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (10)

Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations ⋮ A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation ⋮ Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation ⋮ Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation ⋮ Compact exponential energy-preserving method for the Schrödinger equation in the semiclassical regime ⋮ Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation ⋮ Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation ⋮ A class of momentum-preserving finite difference schemes for the Korteweg-de Vries equation ⋮ Compact Exponential Conservative Approaches for the Schrödinger Equation in the Semiclassical Regimes ⋮ Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations

Cites Work

• Unnamed Item
• A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation
• The discrete variational derivative method based on discrete differential forms
• Multi-symplectic methods for the Itô-type coupled KdV equation
• Conservative finite difference schemes for the Degasperis-Procesi equation
• Line integral methods which preserve all invariants of conservative problems
• An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems
• On symplectic and multisymplectic schemes for the KdV equation
• Energy conservation issues in the numerical solution of the semilinear wave equation
• Symplectic integration of Hamiltonian wave equations
• Symplectic wavelet collocation method for Hamiltonian wave equations
• Energy preserving integration of bi-Hamiltonian partial differential equations
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems
• Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
• Preserving multiple first integrals by discrete gradients
• Multi-Symplectic Method for the Zakharov-Kuznetsov Equation
• Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Time-Fractional Kdv Equation
• Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations
• A new class of energy-preserving numerical integration methods
• Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation

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