On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability

Jesus Alfredo Sierra Nunez, Aslan R. Kasimov, Peter A. Markowich, Rada Maria Weishäupl

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)709-739
Number of pages31
JournalJournal of Nonlinear Science
Volume25
Issue number3
DOIs
StatePublished - Feb 11 2015

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics
  • Engineering(all)

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