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Taras V. Skrypnyk

Publications and source records attributed to Taras V. Skrypnyk.

2 recordsLinked to original sources
arXiv2008

Classical R-Operators and Integrable Generalizations of Thirring Equations

We construct different integrable generalizations of the massive Thirring equations corresponding loop algebras $\widetilde{\mathfrak{g}}^σ$ 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.

nlin.SI↗
arXiv2006

Quasigraded Lie Algebras and Modified Toda Field Equations

We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in "principal" gradation and admit Kostant-Adler-Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda field equations for all series of classical matrix Lie algebras $\mathfrak{g}$.

nlin.SI↗