72 citations · 377 across the 9 of their papers we have counts for
8 papers
KdV hierarchies and quantum Novikov's equations
V. M. Buchstaber, A. V. Mikhailov
This paper begins with a review of the well-known KdV hierarchy, the -th Novikov equation, and its finite hierarchy in the classical commutative case. This finite hierarchy cons…
Quantisation ideals of nonabelian integrable systems
Alexander V. Mikhailov
We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie…
Reduction groups and related integrable difference systems of NLS type
S. Konstantinou-Rizos, A. V. Mikhailov, P. Xenitidis
We extend the reduction group method to the Lax-Darboux schemes associated with nonlinear Schrödinger type equations. We consider all possible finite reduction groups and construct…
Darboux transformations, finite reduction groups and related Yang-Baxter maps
Sotiris Konstantinou-Rizos, Alexander Mikhailov
In this paper we construct Yang-Baxter (YB) maps using Darboux matrices which are invariant under the action of finite reduction groups. We present 6-dimensional YB maps correspond…
Rational Bundles and Recursion Operators for Integrable Equations on A.III-type Symmetric Spaces
Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov +1
We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spa…
Recursion operators, conservation laws and integrability conditions for difference equations
Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis
In this paper we make an attempt to give a consistent background and definitions suitable for the theory of integrable difference equations. We adapt a concept of recursion operato…