Theoretical and Mathematical Physics

, Volume 163, Issue 2, pp 549–586 | Cite as

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

  • A. V. Odesskii
  • V. V. Sokolov


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.”


dispersionless integrable system hydrodynamic reduction Gibbons-Tsarev system 


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© MAIK/Nauka 2010

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASMoscowRussia
  2. 2.Brock UniversitySt. CatharinesCanada

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