
SIGMA 4 (2008), 011, 19 pages arXiv:0802.0184
http://dx.doi.org/10.3842/SIGMA.2008.011
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
Classical ROperators and Integrable Generalizations of Thirring Equations
Taras V. Skrypnyk ^{a, b}
^{a)} SISSA, via Beirut 24, 34014 Trieste, Italy
^{b)} Bogolyubov Institute for Theoretical Physics,
14b Metrologichna Str., Kyiv 03680, Ukraine
Received October 31, 2007, in final form January 18, 2008; Published online February 01, 2008
Abstract
We construct different integrable generalizations of
the massive Thirring equations corresponding loop algebras
g^{σ} in different gradings and
associated ''triangular'' Roperators. We consider the most
interesting cases connected with the Coxeter automorphisms, second
order automorphisms and with ''KostantAdlerSymes''
Roperators. We recover a known matrix generalization of the
complex Thirring equations as a partial case of our construction.
Key words:
infinitedimensional Lie algebras; classical Roperators; hierarchies of integrable equations.
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