The Kupershmidt hydrodynamic chains and lattices

Abstract

This paper is devoted to the very important class of hydrodynamic chains (see [9], [23], [24]) first derived by B. Kupershmidt in [14], later re-discovered by M. Blaszak in [4] (see also [21]). An infinite set of local Hamiltonian structures, hydrodynamic reductions parameterized by the hypergeometric function and reciprocal transformations for the Kupershmidt hydrodynamic chains are described. In honour of Boris Kupershmidt