Geodesic
Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 1, pp. 38-54

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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.
Keywords: Egorov metric, Hamiltonian structure, hydrodynamic type systems, Whitham equations, Benney chain.
Mots-clés : Riemann invariant 
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     author = {M. V. Pavlov and S. P. Tsarev},
     title = {Tri-Hamiltonian {Structures} of {Egorov} {Systems} of {Hydrodynamic} {Type}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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M. V. Pavlov; S. P. Tsarev. Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 1, pp. 38-54. http://geodesic.mathdoc.fr/item/FAA_2003_37_1_a3/