Numerical study of fractional nonlinear Schrodinger equations

Handle URI:
http://hdl.handle.net/10754/594276
Title:
Numerical study of fractional nonlinear Schrodinger equations
Authors:
Klein, Christian; Sparber, Christof; Markowich, Peter A. ( 0000-0002-3704-1821 )
Abstract:
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Klein C, Sparber C, Markowich P (2014) Numerical study of fractional nonlinear Schrodinger equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470: 20140364–20140364. Available: http://dx.doi.org/10.1098/rspa.2014.0364.
Publisher:
The Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue Date:
8-Oct-2014
DOI:
10.1098/rspa.2014.0364
PubMed ID:
25484604
PubMed Central ID:
PMC4241009
Type:
Article
ISSN:
1364-5021; 1471-2946
Sponsors:
C.S. acknowledges support by the NSF through grant no. DMS-1161580. Additional support was provided through the NSF research network Ki-Net.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKlein, Christianen
dc.contributor.authorSparber, Christofen
dc.contributor.authorMarkowich, Peter A.en
dc.date.accessioned2016-01-19T14:44:59Zen
dc.date.available2016-01-19T14:44:59Zen
dc.date.issued2014-10-08en
dc.identifier.citationKlein C, Sparber C, Markowich P (2014) Numerical study of fractional nonlinear Schrodinger equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470: 20140364–20140364. Available: http://dx.doi.org/10.1098/rspa.2014.0364.en
dc.identifier.issn1364-5021en
dc.identifier.issn1471-2946en
dc.identifier.pmid25484604en
dc.identifier.doi10.1098/rspa.2014.0364en
dc.identifier.urihttp://hdl.handle.net/10754/594276en
dc.description.abstractUsing a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.en
dc.description.sponsorshipC.S. acknowledges support by the NSF through grant no. DMS-1161580. Additional support was provided through the NSF research network Ki-Net.en
dc.publisherThe Royal Societyen
dc.subjectDispersionen
dc.subjectFnite time blow-upen
dc.subjectFourier spectral methoden
dc.subjectFractional Laplacianen
dc.subjectNonlinear Schrödinger equationsen
dc.titleNumerical study of fractional nonlinear Schrodinger equationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
dc.identifier.pmcidPMC4241009en
dc.contributor.institutionInstitut de Mathématiques de Bourgogne, 9 avenue Alain SavaryDijon, Franceen
dc.contributor.institutionDepartment of Mathematics, Statistics, and Computer Science, M/C 249, University of Illinois at Chicago, 851 S. Morgan St.Chicago, IL, United Statesen
kaust.authorMarkowich, Peter A.en

Related articles on PubMed

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.