English

On the local systems Hamiltonian in the weakly nonlocal Poisson brackets

Exactly Solvable and Integrable Systems 2009-10-31 v6 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.nlin/0006030,
  title  = {On the local systems Hamiltonian in the weakly nonlocal Poisson brackets},
  author = {A. Ya. Maltsev and S. P. Novikov},
  journal= {arXiv preprint arXiv:nlin/0006030},
  year   = {2009}
}

Comments

45 pages, latex