arXiv Analytics

Sign in

arXiv:1310.2388 [math.NA]AbstractReferencesReviewsResources

On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability

Jesús Sierra, Aslan Kasimov, Peter Markowich, Rada-Maria Weishäupl

Published 2013-10-09Version 1

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.

Comments: 26 pages, 23 figures
Categories: math.NA, math.AP
Related articles:
arXiv:1611.02045 [math.NA] (Published 2016-11-07)
Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method
arXiv:2002.09898 [math.NA] (Published 2020-02-23)
Efficient numerical methods for computing the stationary states of phase field crystal models
arXiv:1812.00980 [math.NA] (Published 2018-12-03)
Well-balanced finite volume schemes for hydrodynamic equations with general free energy

Links

Toolbox