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Nelin. Dinam., 2016, Volume 12, Number 3, Pages 355–367 (Mi nd532)  

This article is cited in 2 scientific papers (total in 2 papers)

Original papers

On an integrable system on the plane with velocity-dependent potential

Yu. A. Grigor'ev, A. P. Sozonov, A. V. Tsiganov

Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia

Abstract: We discuss an algorithmic construction of the auto Bäcklund transformations of HamiltonJacobi equations and possible applications of this algorithm to finding new integrable systems with integrals of motion of higher order in momenta. We explicitly present Bäcklund transformations for two Hamiltonian systems on the plane separable in parabolic and elliptic coordinates.

Keywords: integrable systems, separation of variables, velocity-dependent potentials

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00090 _
Russian Science Foundation 15-11-30007


DOI: https://doi.org/10.20537/nd1603005

Full text: PDF file (377 kB)
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
UDC: 517.9
MSC: 37K35, 53D22, 70H06
Received: 06.06.2016
Accepted:25.06.2016

Citation: Yu. A. Grigor'ev, A. P. Sozonov, A. V. Tsiganov, “On an integrable system on the plane with velocity-dependent potential”, Nelin. Dinam., 12:3 (2016), 355–367

Citation in format AMSBIB
\Bibitem{GriSozTsi16}
\by Yu.~A.~Grigor'ev, A.~P.~Sozonov, A.~V.~Tsiganov
\paper On an integrable system on the plane with velocity-dependent potential
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 3
\pages 355--367
\mathnet{http://mi.mathnet.ru/nd532}
\crossref{https://doi.org/10.20537/nd1603005}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1821100}
\elib{http://elibrary.ru/item.asp?id=27328719}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Tsyganov, “Ob odnoi integriruemoi sisteme na ploskosti s integralom dvizheniya shestoi stepeni po impulsam”, Nelineinaya dinam., 13:1 (2017), 117–127  mathnet  crossref  elib
    2. A. V. Tsiganov, “Bäcklund transformations for the Jacobi system on an ellipsoid”, Theoret. and Math. Phys., 192:3 (2017), 1350–1364  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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