Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein Condensates

TL;DR

This paper introduces a novel algorithm for constructing exact solutions of superfluid flows in inhomogeneous Bose-Einstein condensates by combining similarity reduction and conformal mapping techniques.

Contribution

The authors develop a new method to generate exact analytic solutions for superfluid flows in 2D Bose-Einstein condensates with inhomogeneous potentials.

Findings

The method produces stable superfluid flow solutions.

Several physically relevant examples of flows are demonstrated.

The stability analysis confirms the physical relevance of the solutions.

Abstract

We report a novel algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevskii equation to the one-dimensional nonlinear Schrodinger equation, the latter allowing for exact solutions, with the conformal mapping of the given domain, where the flow is considered, to a half-space. The stability of the obtained flows is addressed. A number of stable and physically relevant examples are described.