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SUMMARY:Orbital stability of a traveling wave of the Gross-Pitaevskii equa
 tion
DTSTART:20260630T091500Z
DTEND:20260630T101500Z
DTSTAMP:20260722T231000Z
UID:indico-event-16224@indico.math.cnrs.fr
DESCRIPTION:Speakers: Frédéric Valet\n\nThe two-dimensional Gross-Pitaev
 skii equation is a non-linear model for the distribution of Bose-Einstein
  condensates. Despite the similarity with the non-linear Schr¨odinger eq
 uation (NLS)\, the non-vanishing condition at infinity induces different 
 inherent structures from the ones of NLS. Unlike the one-dimensional case\
 , it is also not kwown if this non-linear dispersive equation is integrab
 le and the momentum is defined only formally. Furthermore\, a balance bet
 ween the dispersion and the non linearity provide traveling waves. The onl
 y traveling waves with small velocities behave as a vortex-antivortex pai
 r. We approach in the talk the question of orbital stability of those tra
 veling waves. We introduce a new proof by tackling the problem of the defi
 nition of the momentum and by detailing how the non-linearity strongly in
 fluences the ”quadratic” form at infinity. The talk is based on a coll
 aboration with Philippe Gravejat and Eliot Pacherie (CY Cergy Paris Univer
 sité).\n\nhttps://indico.math.cnrs.fr/event/16224/
URL:https://indico.math.cnrs.fr/event/16224/
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