%0 Journal Article
%T On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability
%A Jes¨²s Sierra
%A Aslan Kasimov
%A Peter Markowich
%A Rada-Maria Weish£żupl
%J Mathematics
%D 2013
%I arXiv
%X We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary radially symmetric solutions of the equation are studied and their linear stability with respect to two-dimensional perturbations is analyzed. Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states. Accurate numerical integration is employed to study the general nonlinear evolution of the system from the unstable stationary solutions to the formation of stable vortex patterns.
%U http://arxiv.org/abs/1310.2388v1