Systems of Gibbons-Tsarev type and integrable 3-dimensional models

Details Systems of Gibbons-Tsarev type and integrable 3-dimensional models Systems of Gibbons-Tsarev type and integrable 3-dimensional models

2009-06-18

arxiv.org/abs/0906.3509v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, latex

Scientific paper

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.

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