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Tri-Hamiltonian structures of Egorov systems of hydrodynamic type. (English. Russian original) Zbl 1019.37048

Funct. Anal. Appl. 37, No. 1, 32-45 (2003); translation from Funkts. Anal. Prolozh. 37, No. 1, 38-54 (2003).
Summary: We prove a simple condition under which the metric corresponding to a diagonalizable semi-Hamiltonian hydrodynamic type system belongs to the class of Egorov (potential) metrics. For Egorov diagonal hydrodynamic type systems satisfying natural semisimplicity and homogeneity conditions, we prove necessary and sufficient conditions under which the third structure is local or corresponds to a metric of constant curvature. The results are illustrated by some well-known physical examples of such systems.

MSC:

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q99 Partial differential equations of mathematical physics and other areas of application
76B99 Incompressible inviscid fluids
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