Multi-symplectic Preissmann scheme for a high order wave equation of KdV type

The high order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. Here, the new multi-symplectic formulations for the high order wave equation of KdV type are presented, and the associated local conservation laws are shown. The multi-symplectic discretization of each formulation is exemplified by the multi-symplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the multi-symplectic Preissmann scheme.