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Pade approximations of vortex solutions of the Gross-Pitaevskii equation

Padé approximants are used to find the approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for the uniform condensate and condensates with axisymmetric trapping potentials. The approximate solutions are used to elucidate the annihilation of pair of vortices of opposite circulation by finding the approximation to the streamfunction of the flow generated by such a pair. The critical velocity and minimal separation of vortices are calculated.