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

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

2010-09-14

arxiv.org/abs/1009.2778v1

Theoretical and Mathematical Physics, 2010, Volume 163, Number 2, Pages 549-586

Nonlinear Sciences

Exactly Solvable and Integrable Systems

47 pages, no figures

Scientific paper

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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