Geodesic
On an integrable system on the plane with velocity-dependent potential
Russian journal of nonlinear dynamics, Tome 12 (2016) no. 3, pp. 355-367

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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. 
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     title = {On an integrable system on the plane with velocity-dependent potential},
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Yu. A. Grigor'ev; A. P. Sozonov; A. V. Tsiganov. On an integrable system on the plane with velocity-dependent potential. Russian journal of nonlinear dynamics, Tome 12 (2016) no. 3, pp. 355-367. http://geodesic.mathdoc.fr/item/ND_2016_12_3_a4/