Abstract
We discuss one of the possible finite-dimensional analogues of the general Bäcklund transformation relating different partial differential equations. We show that different Hamilton-Jacobi equations can be obtained from the same Lax matrix. We consider Hénon-Heiles systems on the plane, Neumann and Chaplygin systems on the sphere, and two integrable systems with velocity-dependent potentials as examples.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 183, No. 3, pp. 372–387, June, 2015.
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Sozonov, A.P., Tsiganov, A.V. Bäcklund transformations relating different Hamilton-Jacobi equations. Theor Math Phys 183, 768–781 (2015). https://doi.org/10.1007/s11232-015-0295-x
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DOI: https://doi.org/10.1007/s11232-015-0295-x