34 citations · 122 across the 10 of their papers we have counts for
4 papers · 1 filter
Lie algebras in vortex dynamics and celestial mechanics - IV
A. V. Bolsinov, A. V. Borisov, I. S. Mamaev
The work of A.V. Borisov, A.E. Pavlov, Dynamics and Statics of Vortices on a Plane and a Sphere - I (Reg. & Ch. Dynamics, 1998, Vol. 3, No 1, p.28-39) introduces a naive descriptio…
Dynamics of three vortices on a plane and a sphere -- III. Noncompact case. Problems of collaps and scattering
A. V. Borisov, V. G. Lebedev
In this article we considered the integrable problems of three vortices on a plane and sphere for noncompact case. We investigated explicitly the problems of a collapse and a scatt…
Dynamics of three vortices on a plane and a sphere - II. General compact case
A. V. Borisov, V. G. Lebedev
Integrable problem of three vorteces on a plane and sphere are considered. The classification of Poisson structures is carried out. We accomplish the bifurcational analysis using t…
Dynamics and statics of vortices on a plane and a sphere - I
A. V. Borisov, A. E. Pavlov
In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices…