Physical invariants-preserving compact difference schemes for the coupled nonlinear Schrödinger-KdV equations

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Cites Work

Convergence of a numerical scheme for a coupled Schrödinger-KdV system
Existence of bound states for the coupled Schrödinger-KdV system with cubic nonlinearity
A meshless method for numerical solution of the coupled Schrödinger-KdV equations
The finite element method for the coupled Schrödinger-KdV equations
Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system
Homotopy perturbation method for coupled Schrödinger-KdV equation
Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrödinger-KdV equation
The scalar auxiliary variable (SAV) approach for gradient flows
A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations
Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations
Energy-conserving and time-stepping-varying ESAV-Hermite-Galerkin spectral scheme for nonlocal Klein-Gordon-Schrödinger system with fractional Laplacian in unbounded domains
Well-posedness for the Schrödinger-Korteweg-de Vries system
Dynamics of coupled solitons
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
High-order compact finite difference scheme with two conserving invariants for the coupled nonlinear Schrödinger–KdV equations
The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
Mass-, Energy-, and Momentum-Preserving Spectral Scheme for Klein-Gordon-Schrödinger System on Infinite Domains
Efficient and accurate exponential SAV algorithms with relaxation for dissipative system
Energy stable schemes for the Klein-Gordon-Zakharov equations
High-order Runge-Kutta structure-preserving methods for the coupled nonlinear Schrödinger-KdV equations
Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations

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