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

27 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

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10.1023/B:JOSS.0000044070.34410.17

Cite this

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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.",

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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

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U2 - 10.1023/B:JOSS.0000044070.34410.17

DO - 10.1023/B:JOSS.0000044070.34410.17

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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

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