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Degenerate bi-Hamiltonian structures of hydrodynamic type. (English. Russian original) Zbl 0963.37062

Theor. Math. Phys. 122, No. 2, 247-255 (2000); translation from Teor. Mat. Fiz. 122, No. 2, 294-304 (2000).
This paper is devoted to degenerate bi-Hamiltonian Poisson brackets of hydrodynamic type. It is shown that they are bi-Hamiltonian structures of certain dispersionless rational Lax equations and are related to the notion of a degenerate Frobenius manifold (the natural geometric setting in which the bi-Hamiltonian structure of hydrodynamic systems can be understood is the Frobenius manifold).

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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