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We study the dynamics of vortices with arbitrary topological charges inweakly interacting Bose-Einstein condensates using the Adomian DecompositionMethod to solve the nonlinear Gross-Pitaevskii equation in polar coordinates.The solutions of the vortex equation are expressed in the form of infinitepower series. The power series representations are compared with the exactnumerical solutions of the Gross-Pitaevskii equation for the uniform and theharmonic potential, respectively. We find that there is a good agreementbetween the analytical and the numerical results.

Vortex solutions in atomic Bose-Einstein condensates via the Adomian Decomposition Method