2010/09/14 by Alexander Odesskii, Vladimir Sokolov · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math.AG
paper · pdf · doi:10.1007/s11232-010-0043-1
published as Theoretical and Mathematical Physics, 2010, Volume 163, Number 2, Pages 549-586 · 47 pages, no figures
arxiv created 2010/09/14 · arxiv updated 2015/05/19
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.