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Theoretical and Mathematical Physics

, Volume 187, Issue 3, pp 823–834 | Cite as

Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions

  • A. K. PogrebkovEmail author
Article

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.

Keywords

integrable equation commutator identity reduction 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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