Semiclassical asymptotics for weakly nonlinear Bloch waves

Rémi Carles; Peter Markowich; Christof Sparber

doi:10.1023/B:JOSS.0000044070.34410.17

Semiclassical asymptotics for weakly nonlinear Bloch waves

Rémi Carles, Peter Markowich, Christof Sparber

Computer, Electrical and Mathematical Science and Engineering

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

Original language	English (US)
Pages (from-to)	343-375
Number of pages	33
Journal	Journal of Statistical Physics
Volume	117
Issue number	1-2
DOIs	https://doi.org/10.1023/B:JOSS.0000044070.34410.17
State	Published - Oct 1 2004

Keywords

Bloch eigenvalue problem
Bose-Einstein condensate
Nonlinear Schrödinger equation
WKB-asymptotics

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1023/B:JOSS.0000044070.34410.17

Fingerprint Dive into the research topics of 'Semiclassical asymptotics for weakly nonlinear Bloch waves'. Together they form a unique fingerprint.

Cite this

@article{d6a94c11cee1445c9a94666cd60a8bd6,

title = "Semiclassical asymptotics for weakly nonlinear Bloch waves",

abstract = "We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schr{\"o}dinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.",

keywords = "Bloch eigenvalue problem, Bose-Einstein condensate, Nonlinear Schr{\"o}dinger equation, WKB-asymptotics",

author = "R{\'e}mi Carles and Peter Markowich and Christof Sparber",

year = "2004",

month = oct,

day = "1",

doi = "10.1023/B:JOSS.0000044070.34410.17",

language = "English (US)",

volume = "117",

pages = "343--375",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Semiclassical asymptotics for weakly nonlinear Bloch waves

AU - Carles, Rémi

AU - Markowich, Peter

AU - Sparber, Christof

PY - 2004/10/1

Y1 - 2004/10/1

N2 - We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

AB - We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

KW - Bloch eigenvalue problem

KW - Bose-Einstein condensate

KW - Nonlinear Schrödinger equation

KW - WKB-asymptotics

UR - http://www.scopus.com/inward/record.url?scp=5444243818&partnerID=8YFLogxK

U2 - 10.1023/B:JOSS.0000044070.34410.17

DO - 10.1023/B:JOSS.0000044070.34410.17

M3 - Article

AN - SCOPUS:5444243818

VL - 117

SP - 343

EP - 375

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -

Semiclassical asymptotics for weakly nonlinear Bloch waves

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this