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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 2, Pages 350–382
DOI: https://doi.org/10.4213/tmf10447 (Mi tmf10447) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On a class of quadratic conservation laws for Newton equations in Euclidean space

A. V. Tsiganov, E. O. Porubov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (612 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf10447
Abstract: We discuss quadratic conservation laws for the Newton equations and the corresponding second-order Killing tensors in Euclidean space. In this case, the complete set of integrals of motion consists of polynomials of the second, fourth, sixth, and so on degrees in momenta, which can be constructed using the Lax matrix related to the hierarchy of the multicomponent nonlinear Schrödinger equation.
Keywords: Killing tensors, integrable systems, symmetric spaces.
Funding agency Grant number
Russian Science Foundation 21-11-00141
Gazprom Neft
The work is performed under the financial support of the Russian Science Foundation (grant No. 21-11-00141). The second author (E. O. Porubov) thanks the social investment program “Native cities” of the Public corporation “Gazprom Neft” for supporting the Chebyshev Laboratory of St. Petersburg State University.
Received: 26.01.2023
Revised: 17.04.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 2, Pages 1209–1237
DOI: https://doi.org/10.1134/S0040577923080111
Bibliographic databases:
PACS: 02.30.Ik; 02.40.Ky
MSC: 70H06, 53B21
Language: Russian
Citation: A. V. Tsiganov, E. O. Porubov, “On a class of quadratic conservation laws for Newton equations in Euclidean space”, TMF, 216:2 (2023), 350–382; Theoret. and Math. Phys., 216:2 (2023), 1209–1237
Citation in format AMSBIB
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\by A.~V.~Tsiganov, E.~O.~Porubov
\paper On a~class of quadratic conservation laws for Newton equations in Euclidean space
\jour TMF
\yr 2023
\vol 216
\issue 2
\pages 350--382
\mathnet{http://mi.mathnet.ru/tmf10447}
\crossref{https://doi.org/10.4213/tmf10447}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4634818}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...216.1209T}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 216
\issue 2
\pages 1209--1237
\crossref{https://doi.org/10.1134/S0040577923080111}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85169113389}
Linking options:
  • https://www.mathnet.ru/eng/tmf10447
  • https://doi.org/10.4213/tmf10447
  • https://www.mathnet.ru/eng/tmf/v216/i2/p350
    • This publication is cited in the following 2 articles:
    1. A. V. Tsiganov, “On rotation invariant integrable systems”, Izv. Math., 88:2 (2024), 389–409  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Andrey V. Tsiganov, “Rotations and Integrability”, Regul. Chaotic Dyn., 29:6 (2024), 913–930  mathnet  crossref
    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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    References:41
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