New schemes for the nonlinear Shrödinger equation

摘要

In this paper, a new scheme is derived from a multisymplectic integrator of the nonlinear Shrödinger equation (NLS). We can also call the new scheme multisymplectic scheme. Since multisymplectic integrators can be constructed by using symplectic schemes in both time and space directions, we can use the composition method to get higher-order integrators. Correspondingly, the higher-order composition schemes of the new scheme can be obtained.