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 Nelin. Dinam.: Year: Volume: Issue: Page: Find

 Nelin. Dinam., 2017, Volume 13, Number 1, Pages 117–127 (Mi nd554)

Original papers

On an integrable system on a plane with an integral of motion of sixth order in momenta

A. V. Tsiganov

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

Abstract: In the framework of the Jacobi method we obtain a new integrable system on the plane with a natural Hamilton function and a second integral of motion which is a polynomial of sixth order in momenta. The corresponding variables of separation are images of usual parabolic coordinates on the plane after a suitable Bäcklund transformation. We also present separated relations and prove that the corresponding vector field is bi-Hamiltonian.

Keywords: finite-dimensional integrable systems, separation of variables, Bäcklund transformations

 Funding Agency Grant Number Russian Science Foundation 15-11-30007

DOI: https://doi.org/10.20537/nd1701008

Full text: PDF file (315 kB)
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Document Type: Article
UDC: 517.9
MSC: 37K35, 53D22, 70H06
Accepted:28.12.2016

Citation: A. V. Tsiganov, “On an integrable system on a plane with an integral of motion of sixth order in momenta”, Nelin. Dinam., 13:1 (2017), 117–127

Citation in format AMSBIB
\Bibitem{Tsi17} \by A.~V.~Tsiganov \paper On an integrable system on a plane with an integral of motion of sixth order in momenta \jour Nelin. Dinam. \yr 2017 \vol 13 \issue 1 \pages 117--127 \mathnet{http://mi.mathnet.ru/nd554} \crossref{https://doi.org/10.20537/nd1701008} \elib{http://elibrary.ru/item.asp?id=28841004}