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TMF, 2006, Volume 146, Number 1, Pages 55–64 (Mi tmf2008)  

This article is cited in 16 scientific papers (total in 16 papers)

Integrable Model of Interacting Elliptic Tops

A. V. Zotova, A. M. Levinb

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b P. P. Shirshov institute of Oceanology of RAS

Abstract: We suggest a method for constructing a system of interacting elliptic tops. It is integrable and symplectomorphic to the Calogero–Moser model by construction.

Keywords: integrable systems, algebraic geometry, symplectic geometry

DOI: https://doi.org/10.4213/tmf2008

Full text: PDF file (162 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 146:1, 45–52

Bibliographic databases:


Citation: A. V. Zotov, A. M. Levin, “Integrable Model of Interacting Elliptic Tops”, TMF, 146:1 (2006), 55–64; Theoret. and Math. Phys., 146:1 (2006), 45–52

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Andrey M. Levin, Mikhail A. Olshanetsky, Andrei V. Zotov, “Monopoles and Modifications of Bundles over Elliptic Curves”, SIGMA, 5 (2009), 065, 22 pp.  mathnet  crossref  mathscinet
    2. Andrei V. Zotov, “$1+1$ Gaudin Model”, SIGMA, 7 (2011), 067, 26 pp.  mathnet  crossref  mathscinet
    3. Andrey M. Levin, Mikhail A. Olshanetsky, Andrey V. Smirnov, Andrei V. Zotov, “Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles”, SIGMA, 8 (2012), 095, 37 pp.  mathnet  crossref  mathscinet
    4. Levin A., Olshanetsky M., Smirnov A., Zotov A., “Characteristic Classes and Hitchin Systems. General Construction”, Commun. Math. Phys., 316:1 (2012), 1–44  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Levin A., Olshanetsky M., Smirnov A., Zotov A., “Calogero–Moser Systems for Simple Lie Groups and Characteristic Classes of Bundles”, J. Geom. Phys., 62:8 (2012), 1810–1850  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Levin A. Olshanetsky M. Smirnov A. Zotov A., “Characteristic Classes of Sl(N, C)-Bundles and Quantum Dynamical Elliptic R-Matrices”, J. Phys. A-Math. Theor., 46:3 (2013), 035201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. JETP Letters, 97:1 (2013), 45–51  mathnet  crossref  crossref  isi  elib  elib
    8. A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Gorsky A. Zabrodin A. Zotov A., “Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems”, J. High Energy Phys., 2014, no. 1, 070, 1–28  crossref  mathscinet  isi  scopus  scopus
    11. Levin A. Olshanetsky M. Zotov A., “Planck Constant as Spectral Parameter in Integrable Systems and Kzb Equations”, J. High Energy Phys., 2014, no. 10, 109  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Levin A. Olshanetsky M. Zotov A., “Classical Integrable Systems and Soliton Equations Related To Eleven-Vertex R-Matrix”, Nucl. Phys. B, 887 (2014), 400–422  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Aminov G. Arthamonov S. Smirnov A. Zotov A., “Rational TOP and Its Classical R-Matrix”, J. Phys. A-Math. Theor., 47:30 (2014), 305207  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Levin A. Olshanetsky M. Zotov A., “Relativistic Classical Integrable Tops and Quantum R-Matrices”, J. High Energy Phys., 2014, no. 7, 012  crossref  isi  scopus  scopus
    15. Grekov A. Zotov A., “On R-Matrix Valued Lax pairs For Calogero–Moser Models”, J. Phys. A-Math. Theor., 51:31 (2018), 315202  crossref  isi  scopus  scopus
    16. A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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