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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 183, Number 3, Pages 372–387
DOI: https://doi.org/10.4213/tmf8820 (Mi tmf8820) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Bäcklund transformations relating different Hamilton–Jacobi equations

A. P. Sozonov, A. V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (461 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf8820
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.
Keywords: general Bäcklund transformation, Hamilton–Jacobi equation, separation of variables, Lax matrix.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00061
Saint Petersburg State University 11.38.664.2013
Received: 17.11.2014
Revised: 10.01.2015
English version:
Theoretical and Mathematical Physics, 2015, Volume 183, Issue 3, Pages 768–781
DOI: https://doi.org/10.1007/s11232-015-0295-x
Bibliographic databases:
PACS: 02.90.+p, 03.40.Kf
MSC: 58J72, 70H06
Language: Russian
Citation: A. P. Sozonov, A. V. Tsiganov, “Bäcklund transformations relating different Hamilton–Jacobi equations”, TMF, 183:3 (2015), 372–387; Theoret. and Math. Phys., 183:3 (2015), 768–781
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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