Taras V. Skrypnik, “Classical <nobr>$R$</nobr>-Operators and Integrable Generalizations of Thirring Equations”, SIGMA, 2008, Volume 4,011, 19 pp.

This article is cited in 5 papers

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

Taras V. Skrypnik^ab

^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.

MSC: 17B70; 17B80; 37K10; 37K30; 70H06

Received: October 31, 2007; in final form January 18, 2008; Published online February 1, 2008

Language: English

DOI: 10.3842/SIGMA.2008.011