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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 8, Pages 1340–1349 (Mi zvmmf262)  
This article is cited in 6 scientific papers (total in 6 papers)

The second Hamiltonian structure for a special case of the Lotka–Volterra equations

Yu. V. Bibik

Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
Full-text PDF (1132 kB) Citations (6)
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Abstract: A special case of the Lotka–Volterra equations is considered for which it is possible to find the second Hamiltonian structure that is complementary to the known one. The form of the new Hamiltonian makes it possible to solve the equations by quadratures, which is the main feature of the case under examination. As a consequence, the period can also be represented by quadratures. In terms of the new variables, the equations of motion admit a mechanical analogy with the oscillations of a mass on a nonlinear spring.
Key words: Lotka–Volterra equations, Hamiltonian structure, integrability by quadratures.
Received: 04.04.2006
Revised: 28.12.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 8, Pages 1285–1294
DOI: https://doi.org/10.1134/S0965542507080064
Bibliographic databases:
Document Type: Article
UDC: 519.622.2
Language: Russian
Citation: Yu. V. Bibik, “The second Hamiltonian structure for a special case of the Lotka–Volterra equations”, Zh. Vychisl. Mat. Mat. Fiz., 47:8 (2007), 1340–1349; Comput. Math. Math. Phys., 47:8 (2007), 1285–1294
Citation in format AMSBIB
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\by Yu.~V.~Bibik
\paper The second Hamiltonian structure for a~special case of the Lotka--Volterra equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 8
\pages 1340--1349
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2378179}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 8
\pages 1285--1294
\crossref{https://doi.org/10.1134/S0965542507080064}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548421052}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:44
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