New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems

Details New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems

2006-08-14

arxiv.org/abs/nlin/0608029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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.

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