TY - JOUR
T1 - Semiclassical asymptotics for weakly nonlinear Bloch waves
AU - Carles, Rémi
AU - Markowich, Peter A.
AU - Sparber, Christof
N1 - Funding Information:
2000 Mathematics Subject Classification: 81Q20, 34E13, 34E20, 35Q55. This work was partially supported by the EU network HYKE (Contract No. HPRN-CT-2002-00282), the Wittgenstein Award 2000 of P. A. M. (funded by the Austrian research fund FWF), and the Wissenschaftskolleg Differentialgleichungen (FWF Project No. W8). 1IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes France; e-mail: [email protected] 2Institut für Mathematik der Universität Wien Nordbergstraße 15, A-1090 Vienna, Austria; e-mail: [email protected]; e-mail: [email protected] 3On leave from MAB, Université Bordeaux 1.
PY - 2004/10
Y1 - 2004/10
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
SN - 0022-4715
VL - 117
SP - 343
EP - 375
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1-2
ER -