×

zbMATH — the first resource for mathematics

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.

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] DOI: 10.1017/S0022112087000855 · Zbl 0634.76015
[2] Minzoni A. A., Wave Motion 24 pp 291– (1994) · Zbl 0936.76502
[3] Wang X. P., Physica D 78 pp 241– (1994) · Zbl 0824.35116
[4] Feng B.-F., J. Comput. Appl. Math. 90 pp 95– (1998) · Zbl 0907.65085
[5] Marsden J. E., Commun. Math. Phys. 199 pp 3515– (1998) · Zbl 0951.70002
[6] Zhao P. F., J. Phys. A 33 pp 3613– (2000) · Zbl 0989.37062
[7] DOI: 10.2307/1968645 · Zbl 0013.12002
[8] Bridges TH. J., Math. Proc. Cambridge Philos. Soc. 121 pp 147– (1997) · Zbl 0892.35123
[9] Reich S., J. Chem. Phys. 157 pp 473– (2000)
[10] Atherton R. W., Appl. Math. (Germany) pp 31– (1975)
[11] Garc{ı\'}a P. L., Symp. Math. 14 pp 219– (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.