Integrable pseudopotentials related to elliptic curves

Abstract

We construct integrable pseudopotentials with an arbitrary number of fields in terms of elliptic generalization of hypergeometric functions in several variables. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of integrable (1+1)-dimensional hydrodynamic type systems is also generated by our pseudopotentials.

19 pages, latex

References in corpus (3)

• On integrability of (2+1)-dimensional quasilinear systems
• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• A family of (2+1)-dimensional hydrodynamic type systems possessing pseudopotential

Cited by in corpus (6)

• Integrable (2+1)-dimensional systems of hydrodynamic type
• Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions
• Systems of Gibbons-Tsarev type and integrable 3-dimensional models
• Classification of integrable hydrodynamic chains
• Multi-variable reductions of the dispersionless DKP hierarchy
• Loewner equations and reductions of dispersionless hierarchies