Periodic and quasi-periodic solutions of a four-dimensional singular differential system describing the motion of vortices

Abstract

In this article, we consider a four-dimensional singular differential system that can describe the dynamics of configurations bearing a small number of vortices in atomic Bose-Einstein condensates. On the basis of the topological degree theory and some analysis methods, we prove that such a system has two distinct families of periodic solutions and two distinct families of quasi-periodic solutions. Some results in the literature are generalized and improved.

Keywords

• periodic solutions
• quasi-periodic solutions
• singular differential system
• topological degree theory
• 34c25
• 34a34
• 37n20