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

Handle URI:
http://hdl.handle.net/10754/575641
Title:
On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability
Authors:
Sierra Nunez, Jesus Alfredo; Kasimov, Aslan R.; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Weishäupl, Rada Maria
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Springer Nature
Journal:
Journal of Nonlinear Science
Issue Date:
11-Feb-2015
DOI:
10.1007/s00332-015-9239-8
ARXIV:
arXiv:1310.2388v1
Type:
Article
ISSN:
09388974
Sponsors:
J. S., A. K., and P. M. gratefully acknowledge research support by King Abdullah University of Science and Technology (KAUST). The first author acknowledges the assistance and comments from W. Bao, D. Ketcheson, P. Antonelli, N. Berloff, F. Pinsker, B. Sandstede, B. Oldeman, and the Research Computing Group from KAUST. The work of the last author has been supported by the Hertha-Firnberg Program of the FWF, Grant T402-N13.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSierra Nunez, Jesus Alfredoen
dc.contributor.authorKasimov, Aslan R.en
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorWeishäupl, Rada Mariaen
dc.date.accessioned2015-08-24T08:34:50Zen
dc.date.available2015-08-24T08:34:50Zen
dc.date.issued2015-02-11en
dc.identifier.issn09388974en
dc.identifier.doi10.1007/s00332-015-9239-8en
dc.identifier.urihttp://hdl.handle.net/10754/575641en
dc.description.abstractWe 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.en
dc.description.sponsorshipJ. S., A. K., and P. M. gratefully acknowledge research support by King Abdullah University of Science and Technology (KAUST). The first author acknowledges the assistance and comments from W. Bao, D. Ketcheson, P. Antonelli, N. Berloff, F. Pinsker, B. Sandstede, B. Oldeman, and the Research Computing Group from KAUST. The work of the last author has been supported by the Hertha-Firnberg Program of the FWF, Grant T402-N13.en
dc.publisherSpringer Natureen
dc.subjectBose–Einstein condensateen
dc.subjectCollocation methoden
dc.subjectComplex Gross–Pitaevskii equationen
dc.subjectNumerical continuationen
dc.titleOn the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stabilityen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Nonlinear Scienceen
dc.contributor.institutionFaculty of Mathematics, Vienna University, Oskar-Morgenstern-Platz 1Wien, Austriaen
dc.identifier.arxividarXiv:1310.2388v1en
kaust.authorKasimov, Aslan R.en
kaust.authorMarkowich, Peter A.en
kaust.authorSierra Nunez, Jesus Alfredoen
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