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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 141, Number 1, Pages 38–59
DOI: https://doi.org/10.4213/tmf111 (Mi tmf111) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Integrable Systems Obtained by Puncture Fusion from Rational and Elliptic Gaudin Systems

Yu. B. Chernyakov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Full-text PDF (289 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf111
Abstract: Using the procedure for puncture fusion, we obtain new integrable systems with poles of orders higher than one in the Lax operator matrix and consider the Hamiltonians, symplectic structure, and symmetries of these systems. Using the Inozemtsev limit procedure, we find a Toda-like system in the elliptic case having nontrivial commutation relations between the phase-space variables.
Keywords: integrable systems, Hitchin systems, Lax operator, rational Gaudin models, elliptic Gaudin models, Inozemtsev limit, puncture fusion.
Received: 04.11.2003
Revised: 25.12.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 141, Issue 1, Pages 1361–1380
DOI: https://doi.org/10.1023/B:TAMP.0000043854.15085.00
Bibliographic databases:
Language: Russian
Citation: Yu. B. Chernyakov, “Integrable Systems Obtained by Puncture Fusion from Rational and Elliptic Gaudin Systems”, TMF, 141:1 (2004), 38–59; Theoret. and Math. Phys., 141:1 (2004), 1361–1380
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf111
  • https://doi.org/10.4213/tmf111
  • https://www.mathnet.ru/eng/tmf/v141/i1/p38
    • This publication is cited in the following 5 articles:
    1. Olivier Marchal, Mohamad Alameddine, “Isomonodromic and isospectral deformations of meromorphic connections: the
      sl
      2
      (
      C
      )
      case”, Nonlinearity, 37:11 (2024), 115006  crossref
    2. Ilia Gaiur, Marta Mazzocco, Vladimir Rubtsov, “Isomonodromic Deformations: Confluence, Reduction and Quantisation”, Commun. Math. Phys., 400:2 (2023), 1385  crossref
    3. Alexander Chervov, Gregorio Falqui, Leonid Rybnikov, “Limits of Gaudin Systems: Classical and Quantum Cases”, SIGMA, 5 (2009), 029, 17 pp.  mathnet  crossref  mathscinet  zmath
    4. Petrera, M, “An integrable discretization of the rational su(2) Gaudin model and related systems”, Communications in Mathematical Physics, 283:1 (2008), 227  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Musso F, Petrera M, Ragnisco O, et al, “A rigid body dynamics derived from a class of extended Gaudin models: An integrable discretization”, Regular & Chaotic Dynamics, 10:4 (2005), 363–380  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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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