Multisymplectic Geometry and Multisymplectic Preissman Scheme for the KP Equation

TL;DR

This paper derives the multisymplectic structure of the KP equation using variational principles and formulates a multisymplectic numerical scheme, including a simplified forty-five points version, based on covariant Hamiltonian theories.

Contribution

It introduces a novel multisymplectic formulation of the KP equation directly from variational principles and develops a corresponding numerical scheme.

Findings

Derived multisymplectic structure from variational principles

Formulated a multisymplectic numerical scheme for KP

Simplified to a forty-five points scheme

Abstract

The multisymplectic structure of the KP equation is obtained directly from the variational principal. Using the covariant De Donder-Weyl Hamilton function theories, we reformulate the KP equation to the multisymplectic form which proposed by Bridges. From the multisymplectic equation, we can derive a multisymplectic numerical scheme of the KP equation which can be simplified to multisymplectic forty-five points scheme.