On an integrable system on the plane with velocity-dependent potential
Received 06 June 2016; accepted 25 June 2016
2016, Vol. 12, No. 3, pp. 355-367
Author(s): Grigoryev Y. A., Sozonov A. P., Tsiganov A. V.
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.
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