34 citations · 122 across the 10 of their papers we have counts for
10 papers
Interaction between Kirchhoff vortices and point vortices in an ideal fluid
Alexey V. Borisov, Ivan S. Mamaev
We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is u…
Motion of vortex sources on a plane and a sphere
Alexey V. Borisov, Ivan S. Mamaev
The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A sy…
New periodic solutions for three or four identical vortices on a plane and a sphere
A. V. Borisov, I. S. Mamaev, A. A. Kilin
In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial…
Reduction and chaotic behavior of point vortices on a plane and a sphere
A. V. Borisov, A. A. Kilin, I. S. Mamaev
We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied t…
Superintegrable systems on sphere
A. V. Borisov, I. S. Mamaev
We consider various generalizations of the Kepler problem to three-dimensional sphere , a compact space of constant curvature. These generalizations include, among other thing…
Kovalevskaya Top and Generalizations of Integrable Systems
A. V. Borisov, I. S. Mamaev, A. G. Kholmskaya
Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and Bogoyavlensky systems on a bundle are considered in this paper. Moreover, a method of introduction of separa…