On the local systems Hamiltonian in the weakly nonlocal Poisson brackets

Details On the local systems Hamiltonian in the weakly nonlocal Poisson brackets On the local systems Hamiltonian in the weakly nonlocal Poisson brackets

2000-06-19

arxiv.org/abs/nlin/0006030v6

Physica D: Nonlinear Phenomena, 156 (1-2) (2001), 53-80.

Nonlinear Sciences

Exactly Solvable and Integrable Systems

45 pages, latex

Scientific paper

10.1016/S0167-2789(01)00280-9

We study in this work the important class of nonlocal Poisson Brackets (PB) which we call weakly nonlocal. They appeared recently in some investigations in the Soliton Theory. However there was no theory of such brackets except very special first order case. Even in this case the theory was not developed enough. In particular, we introduce the Physical forms and find Casimirs, Momentum and Canonical forms for the most important Hydrodynamic type PB of that kind and their dependence on the boundary conditions.

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