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Multisymplectic geometry and multisymplectic Preissman scheme for the KP equation. (English) Zbl 1060.37050
Summary: 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.

37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
Full Text: DOI arXiv
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