Padé approximations of solitary wave solutions of the Gross–Pitaevskii equation

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 generalized 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. PACS numbers: 03.75.Lm, 47.37.+q, 67.40.Vs 1.

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