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SIGMA, 2008, Volume 4, 011, 19 pages (Mi sigma264)  

This article is cited in 5 scientific papers (total in 5 papers)

Classical $R$-Operators and Integrable Generalizations of Thirring Equations

Taras V. Skrypnikab

a SISSA, via Beirut 2-4, 34014 Trieste, Italy
b Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., Kyiv 03680, Ukraine

Abstract: We construct different integrable generalizations of the massive Thirring equations corresponding loop algebras $\widetilde{\mathfrak g}^\sigma$ in different gradings and associated “triangular” $R$-operators. We consider the most interesting cases connected with the Coxeter automorphisms, second order automorphisms and with “Kostant–Adler–Symes” $R$-operators. We recover a known matrix generalization of the complex Thirring equations as a partial case of our construction.

Keywords: infinite-dimensional Lie algebras; classical $R$-operators; hierarchies of integrable equations

DOI: https://doi.org/10.3842/SIGMA.2008.011

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Full text: http://emis.mi.ras.ru/.../011
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ArXiv: 0802.0184
MSC: 17B70; 17B80; 37K10; 37K30; 70H06
Received: October 31, 2007; in final form January 18, 2008; Published online February 1, 2008
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Citation: Taras V. Skrypnik, “Classical $R$-Operators and Integrable Generalizations of Thirring Equations”, SIGMA, 4 (2008), 011, 19 pp.

Citation in format AMSBIB
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\by Taras V.~Skrypnik
\paper Classical $R$-Operators and Integrable Generalizations of Thirring Equations
\jour SIGMA
\yr 2008
\vol 4
\papernumber 011
\totalpages 19
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-83055187121}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. V. Skrypnik, “Dual $R$-matrix integrability”, Theoret. and Math. Phys., 155:1 (2008), 633–645  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Błaszak M., Szablikowski B.M., “Classical $R$-matrix theory for bi-Hamiltonian field systems”, J. Phys. A, 42:40 (2009), 404002, 35 pp.  crossref  mathscinet  zmath  isi  scopus
    3. B. A. Dubrovin, T. V. Skrypnik, “Classical double, $R$-operators, and negative flows of integrable hierarchies”, Theoret. and Math. Phys., 172:1 (2012), 911–931  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. Dobrogowska A., “R-Matrix, Lax pair, and Multiparameter Decompositions of Lie Algebras”, J. Math. Phys., 56:11 (2015), 113508  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Skrypnyk T., “Reduction in Soliton Hierarchies and Special Points of Classical R-Matrices”, J. Geom. Phys., 130 (2018), 260–287  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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