Multi-symplectic method for the coupled Schrödinger—KdV equations

Abstract

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.