Geodesic
Bäcklund transformations relating different Hamilton–Jacobi equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 372-387 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: general Bäcklund transformation, Hamilton–Jacobi equation, separation of variables
Mots-clés : Lax matrix. 
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A. P. Sozonov; A. V. Tsiganov. Bäcklund transformations relating different Hamilton–Jacobi equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 372-387. http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a2/

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