Explicit Multi-Symplectic Method for a High Order Wave Equation of KdV Type

Abstract

In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure is constructed for the equation, and the conservation laws of the continuous equation are presented. The multi-symplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.