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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dark Structures on a Torus for the Nonlinear Schro
dinger Model - Jennie D'ambroise (SUNY Old Westbur
y)
DTSTART;TZID=Europe/London:20220718T143000
DTEND;TZID=Europe/London:20220718T150000
UID:TALK176087AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/176087
DESCRIPTION:Authors: \;J. D'Ambroise\, \;R. Carretero
-Gonzalez\, \;P. Schmelcher\, \;P.G. Kevre
kidis\nThe phenomena of Bose-Einstein condensation
(BECs) has been observed on various underlying ge
ometries such as optical lattices with varying sha
pes and symmetries\, rings\, cylinders\, cones and
of particular interest here\, as confined to the
surface of a torus. From a mathematical perspectiv
e it is particularly interesting to explore how th
e various dark and bright nonlinear waves interact
with the underlying geometric properties of the v
arious background spaces in which they lie. \;
In this project we study the existence\, stabilit
y\, and dynamics of vortex structures for the nonl
inear Schr\\"{o}dinger (NLS) equation on the surfa
ce of a torus. \; One can also derive the eff
ective interaction of the vortices\, viewed here a
s point particles\, and the reduced \; particl
e model is shown to be in excellent agreement with
the full NLS evolution. \; A few varieties of
stationary \; vortex dipoles and quadrapoles
are identified and continued along the torus aspec
t ratio and along the frequency parameter of the s
olution. \; In this work the various localizat
ion and stability properties of such solutions are
detailed\, and the windows of stability (and inst
ability) for these solutions are identified. \
;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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