Analytical description of the nonlinear dynamics of Bose-Einstein condensates by means of genetic algorithms

Abstract

In this paper we show that parallel genetic algorithms provide an accurate analytical description of the nonlinear dynamics of a Bose-Einstein condensate. We consider a spherically symmetric condensate subject to periodic and aperiodic parametric excitations and show that the standard variational equation which describe the time-evolution of the condensate has simple analytical solutions. These solutions are obtained using parallel genetic algorithms and allow us to quantify analytically distinct physical processes such as resonant energy transfers and mode-lockings. The observed efficiency of this method for the aforementioned one-dimensional variational equation suggests that this method can be efficiently used for charting the stability spectrum of condensates subject to parametric excitations and possibly for the description of optic waves travelling in nonlinear media.