Pavlov, M. V. Integrability of the egorov systems of hydrodynamic type. (English. Russian original) Zbl 1125.37049 Theor. Math. Phys. 150, No. 2, 225-243 (2007); translation from Teor. Mat. Fiz. 150, No. 2, 263-285 (2007). Summary: We present integrability criterion for the Egorov systems of hydrodynamic type. We find the general solution by the generalized hodograph method and give examples. We discuss a description of triorthogonal curvilinear coordinate systems from the standpoint of reciprocal transformations. Cited in 4 Documents 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) 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:Hamiltonian structure; reciprocal transformation; Egorov metric; system of hydrodynamic type; Riemann invariant; extended hodograph method; generalized hodograph method PDFBibTeX XMLCite \textit{M. V. Pavlov}, Theor. Math. Phys. 150, No. 2, 225--243 (2007; Zbl 1125.37049); translation from Teor. Mat. Fiz. 150, No. 2, 263--285 (2007) Full Text: DOI References: [1] Dubrovin, B. A.; Novikov, S. P., Sov. Math. Dokl., 27, 665-669 (1983) · Zbl 0553.35011 [2] Tsarev, S. P., Sov. Math. 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