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.

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• On the local systems Hamiltonian in the weakly nonlocal Poisson brackets
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• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type
• The Hamiltonian approach in classification and integrability of hydrodynamic chains
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Cited by in corpus (5)

• 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
• Integrable hydrodynamic chains associated with Dorfman Poisson brackets
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions