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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 2, Pages 279–288
DOI: https://doi.org/10.4213/tmf397
(Mi tmf397)
 

This article is cited in 9 scientific papers (total in 9 papers)

Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type

O. I. Mokhov

Landau Institute for Theoretical Physics, Centre for Non-linear Studies
Full-text PDF (231 kB) Citations (9)
References:
Abstract: We prove that two Dubrovin–Novikov Hamiltonian operators are compatible if and only if one of these operators is the Lie derivative of the other operator along a certain vector field. We consider the class of flat manifolds, which correspond to arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. Locally, these manifolds are defined by solutions of a system of nonlinear equations, which is integrable by the method of the inverse scattering problem. We construct the integrable hierarchies generated by arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators.
Keywords: compatible Hamiltonian operators - systems of hydrodynamic type - Lie derivative, integrable hierarchies, local Poisson brackets of hydrodynamic type, flat pencils of metrics.
English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 2, Pages 1557–1564
DOI: https://doi.org/10.1023/A:1021155028895
Bibliographic databases:
Language: Russian
Citation: O. I. Mokhov, “Compatible Dubrovin–Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type”, TMF, 133:2 (2002), 279–288; Theoret. and Math. Phys., 133:2 (2002), 1557–1564
Citation in format AMSBIB
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\by O.~I.~Mokhov
\paper Compatible Dubrovin--Novikov Hamiltonian Operators, Lie Derivative, and Integrable Systems of Hydrodynamic Type
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\pages 279--288
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\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 2
\pages 1557--1564
\crossref{https://doi.org/10.1023/A:1021155028895}
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  • https://www.mathnet.ru/eng/tmf397
  • https://doi.org/10.4213/tmf397
  • https://www.mathnet.ru/eng/tmf/v133/i2/p279
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
     
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