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

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.

preprint2013arXivOpen access
Jesús SierraAslan KasimovPeter MarkowichRada-Maria Weishäupl
math.APmath.NA
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Open access4 authors2 topics
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Jesús SierraAslan KasimovPeter MarkowichRada-Maria Weishäupl

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