New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
New Hamiltonian formalism based on the theory of conjugate curvilinear coordinate nets is established. All formulas are ``mirrored'' to corresponding formulas in the Hamiltonian formalism constructed by B.A. Dubrovin and S.P. Novikov (in a flat case) and E.V. Ferapontov (in a non-flat case). In the ``mirrored-flat'' case the Lagrangian formulation is found. Multi-Hamiltonian examples are presented. In particular Egorov's case, generalizations of local Nutku--Olver's Hamiltonian structure and corresponding Sheftel--Teshukov's recursion operator are presented. An number of Hamiltonian structures of all odd orders is found.
Keywords
Cite
@article{arxiv.nlin/0608029,
title = {New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems},
author = {Maxim V. Pavlov},
journal= {arXiv preprint arXiv:nlin/0608029},
year = {2007}
}