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

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

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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
Pages (from-to)709-739
Number of pages31
JournalJournal of Nonlinear Science
Volume25
Issue number3
DOIs
Publication statusPublished - 1 Jun 2015
Externally publishedYes

Keywords

  • Bose–Einstein condensate
  • Collocation method
  • Complex Gross–Pitaevskii equation
  • Numerical continuation

Fingerprint

Dive into the research topics of 'On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability'. Together they form a unique fingerprint.

Cite this