On the Cubic Lowest Landau Level Equation

TL;DR

This paper investigates the cubic lowest Landau level equation relevant to rotating Bose-Einstein condensates, providing decay bounds, classifying stationary waves, and analyzing their stability.

Contribution

It offers new bounds on decay, classifies stationary solutions with finite zeros, and determines stability conditions using variational methods.

Findings

Decay bounds for stationary solutions

Classification of stationary waves with finite zeros

Identification of stable stationary waves

Abstract

We study dynamical properties of the cubic lowest Landau level equation, which is used in the modeling of fast rotating Bose-Einstein condensates. We obtain bounds on the decay of general stationary solutions. We then provide a classification of stationary waves with a finite number of zeros. Finally, we are able to establish which of these stationary waves are stable, through a variational analysis.