Pavlov, M. V.; Tsarev, S. P. 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. Cited in 17 Documents 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 Keywords:Egorov metric; Hamiltonian structure; hydrodynamic type systems; Riemann invariant; Whitham equations; Benney chain PDFBibTeX XMLCite \textit{M. V. Pavlov} and \textit{S. P. Tsarev}, Funct. Anal. Appl. 37, No. 1, 32--45 (2003; Zbl 1019.37048); translation from Funkts. Anal. Prolozh. 37, No. 1, 38--54 (2003) Full Text: DOI