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SUMMARY:Dark Structures on a Torus for the Nonlinear Schrodinger Model - J
 ennie D'ambroise (SUNY Old Westbury)
DTSTART:20220718T133000Z
DTEND:20220718T140000Z
UID:TALK176087@talks.cam.ac.uk
DESCRIPTION:Authors: &nbsp\;J. D'Ambroise\,&nbsp\;R. Carretero-Gonzalez\,&
 nbsp\;P. Schmelcher\,&nbsp\;P.G. Kevrekidis\nThe phenomena of Bose-Einstei
 n condensation (BECs) has been observed on various underlying geometries s
 uch as optical lattices with varying shapes and symmetries\, rings\, cylin
 ders\, cones and of particular interest here\, as confined to the surface 
 of a torus. From a mathematical perspective it is particularly interesting
  to explore how the various dark and bright nonlinear waves interact with 
 the underlying geometric properties of the various background spaces in wh
 ich they lie.&nbsp\; In this project we study the existence\, stability\, 
 and dynamics of vortex structures for the nonlinear Schr\\"{o}dinger (NLS)
  equation on the surface of a torus. &nbsp\; One can also derive the effec
 tive interaction of the vortices\, viewed here as point particles\, and th
 e reduced&nbsp\; particle model is shown to be in excellent agreement with
  the full NLS evolution.&nbsp\; A few varieties of stationary&nbsp\; vorte
 x dipoles and quadrapoles are identified and continued along the torus asp
 ect ratio and along the frequency parameter of the solution.&nbsp\; In thi
 s work the various localization and stability properties of such solutions
  are detailed\, and the windows of stability (and instability) for these s
 olutions are identified.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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