Geodesic
On an integrable system on a plane with an integral of motion of sixth order in momenta
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 117-127

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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. 
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     author = {A. V. Tsiganov},
     title = {On an integrable system on a plane with an integral of motion of sixth order in momenta},
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     url = {http://geodesic.mathdoc.fr/item/ND_2017_13_1_a7/}
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A. V. Tsiganov. On an integrable system on a plane with an integral of motion of sixth order in momenta. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 117-127. http://geodesic.mathdoc.fr/item/ND_2017_13_1_a7/