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SUMMARY:Uniqueness\, symmetry and nodal sets for a Ginzburg–Landau type 
 problem in an infinite strip
DTSTART:20261001T091500Z
DTEND:20261001T101500Z
DTSTAMP:20261009T040600Z
UID:indico-event-16692@indico.math.cnrs.fr
DESCRIPTION:Speakers: Amandine Aftalion (LMO (Orsay))\n\nThe Ginzburg-Land
 au energy is studied in a specific geometry: an infinite strip with Neuman
 n boundary conditions and under symmetry properties related to very experi
 ments in Bose Einstein condensates.  We show that there is a unique minim
 izer when the width of the strip is below an explicit threshold. This solu
 tion is in fact a one dimensional soliton. Above the threshold\, the solit
 on becomes unstable and we prove the minimizer vanishes at a single point\
 , with a solitonic behaviour at infinity\, therefore very different from 
 a classical vortex. The same solutions are recovered as mountain pass crit
 ical points in a larger symmetry class. We also show that there exist sta
 tionary solutions to the Gross-Pitaevskii equation with k vortices on a tr
 ansverse line\, which bifurcate from the soliton solution as the width of 
 the strip is increased.\nJoint work with L. Nguyen\, and with E. Sandier a
 nd Ph. Gravejat.\n\nhttps://indico.math.cnrs.fr/event/16692/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/16692/
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