Abstract:
We show that the non-Abelian Hirota difference equation is directly related to a commutator identity on an associative algebra. Evolutions generated by similarity transformations of elements of this algebra lead to a linear difference equation. We develop a special dressing procedure that results in an integrable non-Abelian Hirota difference equation and propose two regular reduction procedures that lead to a set of known equations, Abelian or non-Abelian, and also to some new integrable equations.
This research was performed at the Steklov Mathematical Institute of Russian Academy of Sciences and was funded by a grant from the Russian Science Foundation (Project No. 14-50-00005).
Citation:
A. K. Pogrebkov, “Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions”, TMF, 187:3 (2016), 433–446; Theoret. and Math. Phys., 187:3 (2016), 823–834