Multi-symplectic quasi-interpolation method for Hamiltonian partial differential equations

In this paper, we propose a multi-symplectic quasi-interpolation method for solving multi-symplectic Hamiltonian partial differential equations. Based on the method of lines, we first discretize the multi-symplectic PDEs using quasi-interpolation method and then employ appropriate time integrators to obtain the full-discrete system. The local conservation properties including multi-symplectic conservation laws, energy conservation laws and momentum conservation laws are discussed in detail. For illustration, we provide two concrete examples: the nonlinear wave equation and the nonlinear Schrodinger equation. The salient feature of our multi-symplectic quasi-interpolation method is that it is valid both on uniform grids and nonuniform grids. The numerical results show the good accuracy and excellent conservation properties of the proposed method.