Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2016_187_3_a2,
     author = {A. K. Pogrebkov},
     title = {Commutator identities on associative algebras, {the~non-Abelian} {Hirota} difference equation and its reductions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {433--446},
     publisher = {mathdoc},
     volume = {187},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a2/}
}
TY  - JOUR
AU  - A. K. Pogrebkov
TI  - Commutator identities on associative algebras, the~non-Abelian Hirota difference equation and its reductions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 433
EP  - 446
VL  - 187
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a2/
LA  - ru
ID  - TMF_2016_187_3_a2
ER  - 
%0 Journal Article
%A A. K. Pogrebkov
%T Commutator identities on associative algebras, the~non-Abelian Hirota difference equation and its reductions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 433-446
%V 187
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a2/
%G ru
%F TMF_2016_187_3_a2
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/