Geodesic
Integrable $(2+1)$-dimensional systems of hydrodynamic type
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 179-221

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We describe the results that have so far been obtained in the classification problem for integrable $(2+1)$-dimensional systems of hydrodynamic type. The Gibbons–Tsarev (GT) systems are most fundamental here. A whole class of integrable $(2+1)$-dimensional models is related to each such system. We present the known GT systems related to algebraic curves of genus $g=0$ and $g=1$ and also a new GT system corresponding to algebraic curves of genus $g=2$. We construct a wide class of integrable models generated by the simplest GT system, which was not considered previously because it is “trivial”.
Keywords: dispersionless integrable system, hydrodynamic reduction, Gibbons–Tsarev system. 
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     author = {A. V. Odesskii and V. V. Sokolov},
     title = {Integrable $(2+1)$-dimensional systems of hydrodynamic type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--221},
     publisher = {mathdoc},
     volume = {163},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a0/}
}
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A. V. Odesskii; V. V. Sokolov. Integrable $(2+1)$-dimensional systems of hydrodynamic type. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 179-221. http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a0/