Abstract:
We discuss an algorithmic construction of the auto Bäcklund transformations of Hamilton–Jacobi 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.
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
\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://mathscinet.ams.org/mathscinet-getitem?mr=1821100}
\elib{https://elibrary.ru/item.asp?id=27328719}
Linking options:
https://www.mathnet.ru/eng/nd532
https://www.mathnet.ru/eng/nd/v12/i3/p355
This publication is cited in the following 2 articles:
A. V. Tsyganov, “Ob odnoi integriruemoi sisteme na ploskosti s integralom dvizheniya shestoi stepeni po impulsam”, Nelineinaya dinam., 13:1 (2017), 117–127
A. V. Tsiganov, “Bäcklund transformations for the Jacobi system on an ellipsoid”, Theoret. and Math. Phys., 192:3 (2017), 1350–1364
Citation in format AMSBIB
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