53 citations · 193 across the 25 of their papers we have counts for
6 papers · 1 filter
Lax pairs for BKM hierarchy
Andrey Yu. Konyaev, Vladimir S. Matveev
We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cas…
Stäckel problem for non-diagonal Killing tensors: Yano-Patterson lifts, algebra of strong symmetries and quadratic in momenta integrals
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We construct integrable Hamiltonian systems such that functionally independent Poisson commuting integrals are quadratic in the momenta. Unlike the classical Stäckel setting, we al…
On operator fields in the upper triangular Toeplitz form
M. M. Chernin, A. Yu. Konyaev
In this work, we solve the fundamental problem of describing the coordinate transformations that preserve the upper triangular Toeplitz form of the given operator field. Surprising…
On the Linearization of Certain Singularities of Nijenhuis Operators
Andrey Yu. Konyaev
We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in arXiv:1…
Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere whose magnetic 2-form is…
On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We explore the Jordan-Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field $L…