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

Abstract

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.

18 pages, latex

References in corpus (3)

• On integrability of (2+1)-dimensional quasilinear systems
• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• Integrable pseudopotentials related to elliptic curves

Cited by in corpus (7)

• Integrable (2+1)-dimensional systems of hydrodynamic type
• Dispersionless BKP Hierarchy and Quadrant Löwner Equation
• Classification of integrable hydrodynamic chains
• Integrability properties of some symmetry reductions
• Multi-variable reductions of the dispersionless DKP hierarchy
• Loewner equations and reductions of dispersionless hierarchies
• On linear degeneracy of integrable quasilinear systems in higher dimensions