On (2+1)-dimensional hydrodynamic type systems possessing pseudopotential with movable singularities

2007/02/08 by Alexander Odesskii, Vladimir Sokolov, Odesskii, Alexander +1
Mathematics · Physics and Astronomy · #14H70 #17B63 #17B80 #32L81 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA #msc:14H70 #msc:17B63 #msc:17B80 #msc:32L81 #nlin.SI

paper · pdf · doi:10.48550/arxiv.math-ph/0702026

12 pages, latex

arxiv created 2007/04/10 · arxiv updated 2009/12/01

Abstract

A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable systems having pseudopotentials with movable singularities is described by a functional equation, which can be solved explicitly. This allows us to construct interesting examples of integrable hydrodynamic systems for arbitrary N.

Related

• A family of (2+1)-dimensional hydrodynamic type systems possessing pseudopotential
• Integrable pseudopotentials related to generalized hypergeometric functions
• Integrable pseudopotentials related to elliptic curves
• Systems of Gibbons-Tsarev type and integrable 3-dimensional models
• Integrability of the Manakov--Santini hierarchy