Integrable (2+1)-dimensional systems of hydrodynamic type

@article{Odesskii2010IntegrableS,
  title={Integrable (2+1)-dimensional systems of hydrodynamic type},
  author={Alexander Odesskii and Vladimir Vyacheslavovich Sokolov},
  journal={Theoretical and Mathematical Physics},
  year={2010},
  volume={163},
  pages={549-586}
}
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… 
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