Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation

TL;DR

This paper develops Pade approximation methods to model vortex solutions of the Gross-Pitaevskii equation, enabling analysis of solitary waves and vortex nucleation in Bose-Einstein condensates.

Contribution

It introduces rational and generalized rational function approximations for axisymmetric solitary waves in 2D and 3D, advancing the analytical tools for studying vortex dynamics.

Findings

Pade approximants effectively model vortex solutions with various winding numbers.

New mechanism of vortex nucleation identified through solitary wave interactions.

Approximations applicable to both uniform and trapped condensates.

Abstract

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.