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Integrable pseudopotentials related to generalized hypergeometric functions. (English) Zbl 1274.37040
Summary: We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable \((2+1)\)-dimensional hydrodynamic type systems. In two particular cases these systems are equivalent to integrable scalar 3-dimensional equations of second order. An interesting class of integrable \((1+1)\)-dimensional hydrodynamic type systems is also generated by our pseudopotentials.

MSC:
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
17B63 Poisson algebras
17B80 Applications of Lie algebras and superalgebras to integrable systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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