Integrable (2+1)-dimensional systems of hydrodynamic type
Exactly Solvable and Integrable Systems
2015-05-19 v1 Algebraic Geometry
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.
Cite
@article{arxiv.1009.2778,
title = {Integrable (2+1)-dimensional systems of hydrodynamic type},
author = {Alexander Odesskii and Vladimir Sokolov},
journal= {arXiv preprint arXiv:1009.2778},
year = {2015}
}
Comments
47 pages, no figures