This article is cited in 5 scientific papers (total in 5 papers)
Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions
A. K. Pogrebkov
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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.
integrable equation, commutator identity, reduction
|Russian Science Foundation
|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).
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Theoretical and Mathematical Physics, 2016, 187:3, 823–834
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
Citation in format AMSBIB
\paper Commutator identities on associative algebras, the~non-Abelian Hirota difference equation and its reductions
\jour Theoret. and Math. Phys.
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Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.
V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349
A. K. Pogrebkov, “Higher Hirota difference equations and their reductions”, Theoret. and Math. Phys., 197:3 (2018), 1779–1796
A. Pogrebkov, “Hirota difference equation and Darboux system: mutual symmetry”, Symmetry-Basel, 11:3 (2019), 436
A. K. Pogrebkov, “Commutator identities and integrable hierarchies”, Theoret. and Math. Phys., 205:3 (2020), 1585–1592
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