Vortex interaction dynamics in trapped Bose-Einstein condensates
The mathematical model considered in this paper is as follows \[ \displaylines{\displaystyle{\dot{x}_i = -c(t)S_iy_i - b\sum_{k\neq i} S_k{{y_i-y_k}\over{r_{ik}^{\alpha}}}}\text{,}\cr \displaystyle{\dot{y}_i = +c(t)S_ix_i + b\sum_{k\neq i} S_k{{x_i-x_k}\over{r_{ik}^{\alpha}}}}\;,\;i=1,\ldots n,} \] with \(c(t)>0\), \(b>0\), \(\displaystyle{r_{ik} = \sqrt{(x_i-x_k)^2+(y_i-y_k)^2}}\) and \(\alpha>0\) is some parameter that does not affect the basic results. The case \(n=2\) is studied in detail. Exact (closed form) solutions are presented. Also qualitative studies are performed using energy functions and techniques from the analysis of periodic solutions.
scientific article; zbMATH DE number 5989680