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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.

MSC:
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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