Global bifurcation of vortex and dipole solutions in Bose-Einstein condensates

TL;DR

This paper proves the existence of multiple global solution branches, including vortex and dipole solutions, for the Gross-Pitaevskii equation modeling Bose-Einstein condensates with symmetric harmonic traps.

Contribution

It establishes the global bifurcation structure of vortex and dipole solutions in the Gross-Pitaevskii equation, advancing understanding of BEC solution behavior.

Findings

Existence of several global solution branches identified

Vortex and dipole solutions are among the solutions proven to exist

Provides mathematical foundation for long-term behavior analysis of BEC solutions

Abstract

The Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) with symmetric harmonic trap is given in (1). Periodic solutions of (1) play an important role in the understanding of the long term behavior of its solutions. In this note we prove the existence of several global branches of solutions to (1) among which there are vortex solutions and dipole solutions.