O. I. Bogoyavlenskij, A. P. Reynolds, “Criteria for existence of a Hamiltonian structure”, Regul. Chaotic Dyn., 2010, Volume 15, Issue 4-5,Pages <nobr>431

This article is cited in 5 papers

On the 60th birthday of professor V.V. Kozlov

Criteria for existence of a Hamiltonian structure

O. I. Bogoyavlenskij, A. P. Reynolds

Department of Mathematics, Queen's University, Kingston, K7L 3N6, Canada

Abstract: The necessary and sufficient conditions are derived for the existence of a Hamiltonian structure for 3-component non-diagonalizable systems of hydrodynamic type. The conditions are formulated in terms of tensor invariants defined by the metric $h_{ij}(u)$ constructed from the Haantjes (1,2)-tensor.

Keywords: Poisson brackets, conformally flat metric, covariant derivatives, Weyl–Schouten equations, Haantjes tensor.

MSC: 35L60

Received: 01.10.2009
Accepted: 10.10.2009

Language: English

DOI: 10.1134/S1560354710040039