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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 212, Number 1, Pages 95–108
DOI: https://doi.org/10.4213/tmf10215 (Mi tmf10215) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On noncompact bifurcation in one generalized model of vortex dynamics

G. P. Palshin

Moscow Institute for Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
Full-text PDF (752 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf10215
Abstract: A generalized model of Hamiltonian mechanics is considered. It includes two special cases: a model of the dynamics of three magnetic vortices in ferromagnets and a model of the dynamics of three hydrodynamic vortices in a perfect fluid. A constraint is imposed on the system by fixing one of the vortices at the point of origin. The system of the constrained problem of three magnetic vortices is a completely Liouville-integrable Hamiltonian system with two degrees of freedom. For this system, we find an augmented bifurcation diagram, perform a reduction to a system with one degree of freedom, and investigate level curves of the reduced Hamiltonian in detail. The obtained results show the presence of noncompact bifurcations and a noncritical bifurcation line.
Keywords: vortex dynamics, magnetic vortices, completely integrable Hamiltonian system, augmented bifurcation diagram, noncompact surgery, noncritical bifurcation curve.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00399
This paper was supported by the Russian Foundation for Basic Research grant No. 20-01-00399.
Received: 28.11.2021
Revised: 20.02.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 212, Issue 1, Pages 972–983
DOI: https://doi.org/10.1134/S0040577922070078
Bibliographic databases:
Document Type: Article
MSC: 76M23, 37J35, 37J06, 34A05
Language: Russian
Citation: G. P. Palshin, “On noncompact bifurcation in one generalized model of vortex dynamics”, TMF, 212:1 (2022), 95–108; Theoret. and Math. Phys., 212:1 (2022), 972–983
Citation in format AMSBIB
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\by G.~P.~Palshin
\paper On noncompact bifurcation in one generalized model of vortex dynamics
\jour TMF
\yr 2022
\vol 212
\issue 1
\pages 95--108
\mathnet{http://mi.mathnet.ru/tmf10215}
\crossref{https://doi.org/10.4213/tmf10215}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461546}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022TMP...212..972P}
\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 212
\issue 1
\pages 972--983
\crossref{https://doi.org/10.1134/S0040577922070078}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85134250965}
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  • https://www.mathnet.ru/eng/tmf/v212/i1/p95
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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