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 hij(u) constructed from the Haantjes (1,2)-tensor.
\Bibitem{BogRey10}
\by O. I. Bogoyavlenskij, A. P. Reynolds
\paper Criteria for existence of a Hamiltonian structure
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 4-5
\pages 431--439
\mathnet{http://mi.mathnet.ru/rcd508}
\crossref{https://doi.org/10.1134/S1560354710040039}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2679757}
\zmath{https://zbmath.org/?q=an:1252.35187}
Linking options:
https://www.mathnet.ru/eng/rcd508
https://www.mathnet.ru/eng/rcd/v15/i4/p431
This publication is cited in the following 5 articles:
O. I. Mokhov, N. A. Pavlenko, “Classification of the associativity equations with a first-order Hamiltonian operator”, Theoret. and Math. Phys., 197:1 (2018), 1501–1513
O. I. Mokhov, N. A. Strizhova, “Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin–Novikov type”, Russian Math. Surveys, 73:1 (2018), 175–177
V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Proc. Steklov Inst. Math., 294 (2016), 222–232
A.P. Reynolds, O.I. Bogoyavlenskij, “Lie algebra structures for four-component Hamiltonian hydrodynamic type systems”, Journal of Geometry and Physics, 61:12 (2011), 2400
Citation in format AMSBIB
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