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arxiv: 0906.3509 · v1 · submitted 2009-06-18 · 🌊 nlin.SI · hep-th· math.AG· math.AP

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

classification 🌊 nlin.SI hep-thmath.AGmath.AP
keywords systemsgibbons-tsarev-typedimensionalhydrodynamic-typeintegrableclassclassificationconstract
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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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