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

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.