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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 186, Number 3, Pages 443–455
DOI: https://doi.org/10.4213/tmf8948 (Mi tmf8948) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Two integrable systems with integrals of motion of degree four

A. V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (384 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf8948
Abstract: We discuss the possibility of using second-order Killing tensors to construct Liouville-integrable Hamiltonian systems that are not Nijenhuis integrable. As an example, we consider two Killing tensors with a nonzero Haantjes torsion that satisfy weaker geometric conditions and also three-dimensional systems corresponding to them that are integrable in Euclidean space and have two quadratic integrals of motion and one fourth-order integral in momenta.
Keywords: Hamilton–Jacobi equation, separation of variables, Killing tensor.
Funding agency Grant number
Russian Science Foundation 15-11-30007
This work was supported by the Russian Science Foundation under grant 15-11-30007.
Received: 13.04.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 186, Issue 3, Pages 383–394
DOI: https://doi.org/10.1134/S0040577916030077
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik; 02.40.Ky
MSC: 70H06, 53B21
Language: Russian
Citation: A. V. Tsiganov, “Two integrable systems with integrals of motion of degree four”, TMF, 186:3 (2016), 443–455; Theoret. and Math. Phys., 186:3 (2016), 383–394
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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