6 papers · 1 filter
Finite dimensional reductions of integrable differential-difference equations
Alexander Mikhailov
Integrable partial differential equations, such as the Korteweg--De Vries (KdV) equation, admit infinite hierarchies of commuting higher symmetries. Their symmetry reductions give…
Integrable Volterra hierarchies over nonabelian algebras
J. P. Wang, S. Carpentier, A. V. Mikhailov
Known integrable systems with noncommutative dependent variables are typically formulated over free associative algebras, quantum algebras, or Grassmann algebras. For differential-…
Algebraic quantisation approach to integrable differential-difference equations
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
We develop an algebraic quantisation approach, based on quantisation ideals, and apply it to integrable non-Abelian differential--difference equations. We show that the Toda hierar…
Discrete integrable principal chiral field model and its involutive reduction
Jan L. Cieśliński, Alexander V. Mikhailov, Maciej Nieszporski +1
We discuss an integrable discretization of the principal chiral field models equations and its involutive reduction. We present a Darboux transformation and general construction of…
Commutative Poisson algebras from deformations of noncommutative algebras
Alexander V. Mikhailov, Pol Vanhaecke
It is well-known that a formal deformation of a commutative algebra leads to a Poisson bracket on and that the classical limit of a derivation on the…
Hamiltonians for the quantised Volterra hierarchy
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
This paper builds upon our recent work, published in Lett. Math. Phys., 112: 94, 2022, where we established that the integrable Volterra lattice on a free associative algebra and t…