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Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 433-446 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Commutator identities on associative algebras, {the~non-Abelian} {Hirota} difference equation and its reductions},
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A. K. Pogrebkov. Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 433-446. http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a2/

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