  Pade approximants are used to find approximate vortex solutions of any
winding number in the context of Gross-Pitaevskii equation for a uniform
condensate and condensates with axisymmetric trapping potentials. Rational
function and generalised rational function approximations of axisymmetric
solitary waves of the Gross-Pitaevskii equation are obtained in two and three
dimensions. These approximations are used to establish a new mechanism of
vortex nucleation as a result of solitary wave interactions.
