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28 March 2024
 
  » arxiv » nlin/0608029

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New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems
Maxim V. Pavlov ;
Date 14 Aug 2006
Subject Exactly Solvable and Integrable Systems
AbstractNew 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.
Source arXiv, nlin/0608029
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