Local energy-preserving scalar auxiliary variable approaches for general multi-symplectic Hamiltonian PDEs

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) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

On symplectic and multisymplectic schemes for the KdV equation
Symplectic and multisymplectic numerical methods for Maxwell's equations
Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
Multi-symplectic integration of the Camassa-Holm equation
Splitting multisymplectic integrators for Maxwell's equations
Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations
Local structure-preserving algorithms for partial differential equations
Backward error analysis for multi-symplectic integration methods
Finite volume methods for multi-symplectic PDEs
Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
The scalar auxiliary variable (SAV) approach for gradient flows
Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
Linearly implicit local energy-preserving algorithm for a class of multi-symplectic Hamiltonian PDEs
Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs
Symplectic wavelet collocation method for Hamiltonian wave equations
General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system
Simulating Hamiltonian Dynamics
A new explicit multisymplectic scheme for the regularized long-wave equation
Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows
Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables
Linearly Implicit Local and Global Energy-Preserving Methods for PDEs with a Cubic Hamiltonian
Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows
The Multisymplectic Diamond Scheme
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs
Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach

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