4 papers
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-…
Arithmetic Supports of Lax Difference Hierarchies
Sylvain Carpentier
We classify monic finite-band scalar difference operators with independent coefficients admitting infinitely many support-preserving flows. We prove that such operators are complet…
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…
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…