English

Classical R-Operators and Integrable Generalizations of Thirring Equations

Exactly Solvable and Integrable Systems 2008-12-19 v1 Mathematical Physics math.MP

Abstract

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

Keywords

Cite

@article{arxiv.0802.0184,
  title  = {Classical R-Operators and Integrable Generalizations of Thirring Equations},
  author = {Taras V. Skrypnyk},
  journal= {arXiv preprint arXiv:0802.0184},
  year   = {2008}
}

Comments

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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