We review the role of Gibbons-Tsarev-type systems in classification of integrable multi-dimensional hydrodynamic-type systems. Our main observation is an universality of Gibbons-Tsarev-type systems. We also constract explicitly a wide class of 3-dimensional hydrodynamic-type systems corresponding to the simplest possible Gibbons-Tsarev-type system.
- Pub Date:
- June 2009
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory;
- Mathematics - Algebraic Geometry;
- Mathematics - Analysis of PDEs
- 18 pages, latex