Integrable (2+1)-dimensional systems of hydrodynamic type |
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Authors: | A. V. Odesskii V. V. Sokolov |
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Affiliation: | 1.Landau Institute for Theoretical Physics,RAS,Moscow,Russia;2.Brock University,St. Catharines,Canada |
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Abstract: | 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.” |
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