Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

Handle URI:
http://hdl.handle.net/10754/563715
Title:
Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation
Authors:
Hadj Selem, Fouad; Hajaiej, Hichem; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Trabelsi, Saber
Abstract:
This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Nature
Journal:
Milan Journal of Mathematics
Issue Date:
26-Aug-2014
DOI:
10.1007/s00032-014-0227-5
Type:
Article
ISSN:
14249286
Sponsors:
H. Hajaiej would like to thank NPST for its support through the research project number MA1716. The research of P. A. Markowich and S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.
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.authorHadj Selem, Fouaden
dc.contributor.authorHajaiej, Hichemen
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorTrabelsi, Saberen
dc.date.accessioned2015-08-03T12:07:32Zen
dc.date.available2015-08-03T12:07:32Zen
dc.date.issued2014-08-26en
dc.identifier.issn14249286en
dc.identifier.doi10.1007/s00032-014-0227-5en
dc.identifier.urihttp://hdl.handle.net/10754/563715en
dc.description.abstractThis paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.en
dc.description.sponsorshipH. Hajaiej would like to thank NPST for its support through the research project number MA1716. The research of P. A. Markowich and S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.en
dc.publisherSpringer Natureen
dc.titleVariational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equationen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalMilan Journal of Mathematicsen
dc.contributor.institutionFrench Atomic Energy Commission, NeurospinSaclay, Franceen
dc.contributor.institutionDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455Riyadh, Saudi Arabiaen
kaust.authorMarkowich, Peter A.en
kaust.authorTrabelsi, Saberen
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