Pavlov, M. V. Classifying integrable Egoroff hydrodynamic chains. (English) Zbl 1178.37087 Theor. Math. Phys. 138, No. 1, 45-58 (2004); translation from Teor. Mat. Fiz. 138, No. 1, 55-70 (2004). Summary: We introduce the notion of Egoroff hydrodynamic chains. We show how they are related to integrable \((2+1)\)-dimensional equations of hydrodynamic type. We classify these equations in the simplest case. We find \((2+1)\)-dimensional equations that are not just generalizations of the already known Khokhlov-Zabolotskaya and Boyer-Finley equations but are much more involved. These equations are parameterized by theta functions and by solutions of the Chazy equations. We obtain analogues of the dispersionless Hirota equations. Cited in 16 Documents MSC: 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:hydrodynamic chains and lattices; Egoroff integrable systems; dispersionless hirota equations; tau function; \((2+1)\)-dimensional dispersionless equations; chazy equation; theta function PDFBibTeX XMLCite \textit{M. V. Pavlov}, Theor. Math. Phys. 138, No. 1, 45--58 (2004; Zbl 1178.37087); translation from Teor. Mat. Fiz. 138, No. 1, 55--70 (2004) Full Text: DOI