Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets

Details Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets

2006-07-05

arxiv.org/abs/nlin/0607003v2

JMP, v. 47, no. 1 (2006)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages

Scientific paper

We characterize a class of integrable Hamiltonian hydrodynamic chains, based on the necessary condition for the integrability provided by the vanishing of the Haantjes tensor. We prove that the vanishing of the first few components of the Haantjes tensor is already sufficiently restrictive, and allows a complete description of the corresponding Hamiltonian densities. In each of the cases we were able to explicitly construct a generating function for conservation laws, thus establishing the integrability.

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