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Multi-symplectic structures and wave propagation. (English) Zbl 0892.35123
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.
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.

35Q35 PDEs in connection with fluid mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
49S05 Variational principles of physics
35A15 Variational methods applied to PDEs
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