Multisymplectic geometry and multisymplectic Preissman scheme for the KP equation

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 was proposed by Bridges. From the multisymplectic equation, we can derive a multisymplectic numerical scheme of the KP equation which can be simplified to the multisymplectic 45 points scheme.

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