Geodesic
Classifying Integrable Egoroff Hydrodynamic Chains
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 1, pp. 55-70

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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.
Keywords: hydrodynamic chains and lattices, Egoroff integrable systems, dispersionless Hirota equations, tau function. 
@article{TMF_2004_138_1_a4,
     author = {M. V. Pavlov},
     title = {Classifying {Integrable} {Egoroff} {Hydrodynamic} {Chains}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {55--70},
     publisher = {mathdoc},
     volume = {138},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_1_a4/}
}
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M. V. Pavlov. Classifying Integrable Egoroff Hydrodynamic Chains. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 1, pp. 55-70. http://geodesic.mathdoc.fr/item/TMF_2004_138_1_a4/