6 papers
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 a…
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…
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 Separation of Variables for Symmetric Spaces of Rank1
Alexey Bolsinov, Holger R. Dullin, Vladimir. S. Matveev +1
We study existence and nonexistence of diagonal and separating coordinates for Riemannian symmetric spaces of rank 1. We generalize the results of Gauduchon and Moroianu, 2020, by…
Research problems on relations between Nijenhuis geometry and integrable systems
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The paper surveys open problems and questions related to interplay between the theory of integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis geome…
Finite-dimensional reductions and finite-gap type solutions of multicomponent integrable PDEs
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known…