Hamiltonian-preserving schemes for the two-dimensional fractional nonlinear Schrödinger wave equations

The focus of this paper is to construct structure-preserving numerical methods for the fractional nonlinear Schrodinger wave equations in two dimensions. We first develop the Hamiltonian structure of the studied problem by virtue of the variational principle of the functional with fractional Laplacian. A fully-discrete numerical scheme is then proposed by applying the partitioned averaged vector field plus method and the Fourier pseudo-spectral method to the resulting Hamiltonian system. The obtained fully-discrete scheme is proved to be energy-preserving and mass-preserving in discrete sense. For comparison, more numerical methods are also listed. Finally, several numerical experiments are given to support our theoretical results.