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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 139, Number 2, Pages 225–244
DOI: https://doi.org/10.4213/tmf58 (Mi tmf58) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Toda Chains in the Jacobi Method

A. V. Tsiganov

St. Petersburg State University, Faculty of Physics
Full-text PDF (289 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf58
Abstract: We use the Jacobi method to construct various integrable systems, such as the Stдckel systems and Toda chains, related to various root systems. We find canonical transformations that relate integrals of motion for the generalized open Toda chains of types Bn, Cn, and Dn.
Keywords: integrable systems, Hamilton–Jacobi equation, separation of variables, Toda chains.
Received: 19.05.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 139, Issue 2, Pages 636–653
DOI: https://doi.org/10.1023/B:TAMP.0000026181.79622.af
Bibliographic databases:
Language: Russian
Citation: A. V. Tsiganov, “Toda Chains in the Jacobi Method”, TMF, 139:2 (2004), 225–244; Theoret. and Math. Phys., 139:2 (2004), 636–653
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf58
  • https://doi.org/10.4213/tmf58
  • https://www.mathnet.ru/eng/tmf/v139/i2/p225
    • This publication is cited in the following 8 articles:
    1. A V Tsiganov, “Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres”, Nonlinearity, 35:10 (2022), 5357  crossref
    2. Zhang H., “On Superintegrable Systems With a Position-Dependent Mass in Polar-Like Coordinates”, Chin. Phys. B, 29:10 (2020), 100201  crossref  isi
    3. Zhang H., Hao Q.-Y., “Eisenhart Lift For Euler'S Problem of Two Fixed Centers”, Appl. Math. Comput., 350 (2019), 305–312  crossref  mathscinet  isi  scopus
    4. A. V. Tsyganov, “Razdelenie peremennykh dlya odnogo obobscheniya sistemy Chaplygina na sfere”, Nelineinaya dinam., 11:1 (2015), 179–185  mathnet  elib
    5. Andrey V. Tsiganov, “Simultaneous Separation for the Neumann and Chaplygin Systems”, Regul. Chaotic Dyn., 20:1 (2015), 74–93  mathnet  crossref  mathscinet  zmath
    6. A. P. Sozonov, A. V. Tsiganov, “Bäcklund transformations relating different Hamilton–Jacobi equations”, Theoret. and Math. Phys., 183:3 (2015), 768–781  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Tsiganov A., “Integrable Euler TOP and Nonholonomic Chaplygin Ball”, Journal of Geometric Mechanics, 3:3 (2011), 337–362  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Tsiganov, AV, “On maximally superintegrable systems”, Regular & Chaotic Dynamics, 13:3 (2008), 178  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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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