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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 177, Number 3, Pages 468–481
DOI: https://doi.org/10.4213/tmf8556 (Mi tmf8556) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Separation of variables for some systems with a fourth-order integral of motion

Yu. A. Grigor'ev, V. A. Khudobakhshov, A. V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (412 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf8556
Abstract: We construct separation variables for Yehia's integrable deformations of the Kovalevskaya top and the Chaplygin system on a sphere. In the general case, the corresponding quadratures are given by the Abel–Jacobi map on a two-dimensional submanifold of the Jacobian of a genus-three algebraic curve, which is not hyperelliptic.
Keywords: bi-Hamiltonian geometry, separation of variables, Kovalevskaya top.
Received: 23.05.2013
English version:
Theoretical and Mathematical Physics, 2013, Volume 177, Issue 3, Pages 1680–1692
DOI: https://doi.org/10.1007/s11232-013-0126-x
Bibliographic databases:
PACS: 45.20.Jj, 45.40.−f, 45.50.−j, 02.30.Ik
MSC: 70H20; 70H06; 37K10;
Language: Russian
Citation: Yu. A. Grigor'ev, V. A. Khudobakhshov, A. V. Tsiganov, “Separation of variables for some systems with a fourth-order integral of motion”, TMF, 177:3 (2013), 468–481; Theoret. and Math. Phys., 177:3 (2013), 1680–1692
Citation in format AMSBIB
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    • This publication is cited in the following 1 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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