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Zbl 0892.35123
Bridges, Thomas J.
Multi-symplectic structures and wave propagation. (English)
[J] Math. Proc. Camb. Philos. Soc. 121, No.1, 147-190 (1997). ISSN 0305-0041; ISSN 1469-8064/e

A Hamiltonian structure is presented, which generalizes classical Hamiltonian structure, by assigning a distinct symplectic operator for each unbounded space direction and time, of a Hamiltonian evolution equation on one or more space dimensions. This generalization, called multi-symplectic structures, is shown to be natural for dispersive wave propagation problems.\par The nonlinear Schrödinger equation and the water-wave problem are characterized as Hamiltonian systems on a multi-symplectic structure, for example. Further ramifications of the generalized symplectic structure of theoretical and practical interest are also discussed.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
37J99 Finite-dimensional Hamiltonian etc. systems
49S05 Variational principles of physics
35A15 Variational methods (PDE)

Keywords: Hamiltonian structure; multi-symplectic structures; dispersive wave propagation problems; nonlinear Schrödinger equation; water-wave problem

Cited in: Zbl 1166.65062

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