Integrable (2+1)-dimensional systems of hydrodynamic type
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.”
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- May 2010
- DOI:
- 10.1007/s11232-010-0043-1
- arXiv:
- arXiv:1009.2778
- Bibcode:
- 2010TMP...163..549O
- Keywords:
-
- dispersionless integrable system;
- hydrodynamic reduction;
- Gibbons-Tsarev system;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematics - Algebraic Geometry
- E-Print:
- 47 pages, no figures