Seminar talk, 17 February 2016
Speaker: Maxim Pavlov
Title: New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems
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. A number of Hamiltonian structures of all odd orders is found.
M.Pavlov, New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems, arXiv:nlin/0608029