The Kupershmidt hydrodynamic chains and lattices

Abstract

This paper is devoted to the very important class of hydrodynamic chains first derived by B. Kupershmidt and later re-discovered by M. Blaszak. An infinite set of local Hamiltonian structures, hydrodynamic reductions parameterized by the hypergeometric function and reciprocal transformations for the Kupershmidt hydrodynamic chains are described.

References in corpus (2)

• The Hamiltonian approach in classification and integrability of hydrodynamic chains
• Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains

Cited by in corpus (4)

• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• On Kernel Formulas and Dispersionless Hirota Equations
• Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions