  We study the dynamics of vortices with arbitrary topological charges in
weakly interacting Bose-Einstein condensates using the Adomian Decomposition
Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates.
The solutions of the vortex equation are expressed in the form of infinite
power series. The power series representations are compared with the exact
numerical solutions of the Gross-Pitaevskii equation for the uniform and the
harmonic potential, respectively. We find that there is a good agreement
between the analytical and the numerical results.
