Multi-Symplectic Fourier Pseudospectral Method for a Higher Order Wave Equation of KdV Type

Abstract

The higher order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. In this work, multi-symplectic formulations for the higher order wave equation of KdV type are presented, and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is calculated by the multi-symplectic Fourier pseudospectral scheme. Numerical experiments are carried out, which verify the efficiency of the Fourier pseudospectral method.