Classical R-Operators and Integrable Generalizations of Thirring Equations

TL;DR

This paper develops new integrable generalizations of the massive Thirring equations using classical R-operators and loop algebra automorphisms, expanding the mathematical framework of these models.

Contribution

It introduces novel integrable models of Thirring equations based on loop algebra gradings and R-operators, including cases related to Coxeter automorphisms and Kostant-Adler-Symes methods.

Findings

Constructed integrable generalizations of Thirring equations.

Connected models with Coxeter and second order automorphisms.

Recovered known matrix generalization as a special case.

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.