Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets
Exactly Solvable and Integrable Systems
2015-06-26 v2 Adaptation and Self-Organizing Systems
Abstract
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.
Keywords
Cite
@article{arxiv.nlin/0607003,
title = {Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets},
author = {E. V. Ferapontov and K. R. Khusnutdinova and D. G. Marshall and M. V. Pavlov},
journal= {arXiv preprint arXiv:nlin/0607003},
year = {2015}
}
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14 pages