On multisymplecticity of Sinc-Gauss-Legendre collocation discretizations for some Hamiltonian PDEs

In this paper, a new multisymplectic scheme based on Sinc collocation discretization in space and Gauss-Legendre collocation discretization in time for some Hamiltonian PDEs is developed. The scheme preserves the multisymplectic geometry structure exactly by satisfying the discrete multisymplectic conservation law. Moreover, the discrete energy and momentum conservative properties of the multisymplectic integrator are also discussed. In order to testify the superiority of the multisymplectic method, it is applied to nonlinear Dirac equation. Numerical experiments are given to illustrate the accuracy of the approximation and the conserved quantities.