Multi-symplectic method for the coupled Schrödinger-KdV equations

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrödinger-KdV equations (CSKE) with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral (MSFP) scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson (CN) method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.