110 citations · 608 across the 39 of their papers we have counts for
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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…
Singularities of bi-Hamiltonian systems
Alexey Bolsinov, Anton Izosimov
We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of line…
Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
Alexey V. Bolsinov, Vladimir S. Matveev, Giuseppe Pucacco
We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of…
Geodesics on the Ellipsoid and Monodromy
Chris M. Davison, Holger R. Dullin, Alexey V. Bolsinov
The equations for geodesic flow on the ellipsoid are well known, and were first solved by Jacobi in 1838 by separating the variables of the Hamilton-Jacobi equation. In 1979 Moser…
Magnetic Flows on Homogeneous Spaces
Alexey V. Bolsinov, Bozidar Jovanovic
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-com…
Magnetic Geodesic Flows on Coadjoint Orbits
Alexey V. Bolsinov, Bozidar Jovanovic
We describe a class of completely integrable -invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group with magnetic field given by the Kiril…