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

Alexander Odesskii; Vladimir Sokolov

doi:10.1007/s11232-010-0043-1

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arXiv · 1009.2778

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

Alexander Odesskii·Vladimir Sokolov

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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 systems of Gibbons--Tsarev type are the 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 in a sense trivial.

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Alexander Odesskii, Vladimir Sokolov. 2010-09-14. Integrable (2+1)-dimensional systems of hydrodynamic type. https://doi.org/10.1007/s11232-010-0043-1

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