[NT/RBRC Seminar] Bright and Dark Structures on a Torus for the Nonlinear Schr ̈odinger Model

by Prof. Jennie D'Ambroise (SUNY old westbury )

Friday 26 Apr 2024, 11:00 → 13:00 US/Eastern

Large seminar room (https://bnl.zoomgov.com/j/1614715193?pwd=WkwxODVWdzZzb29zQnZRVGp3VTBDQT09)

The phenomena of Bose-Einstein condensation (BECs) has been observed on various under-
lying geometries such as optical lattices with varying shapes and symmetries, rings, cylinders,

cones and of particular interest here, as confined to the surface of a torus. From a mathe-
matical 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 which they lie. In this project we study the existence, stability, and dynamics of
bright solitons and vortex structures for the nonlinear Schr ̈odinger (NLS) equation on the
surface of a torus. One can also derive the effective interaction of the vortices, viewed as
point particles, and the reduced particle model is shown to be in excellent agreement with
the full NLS evolution. A few varieties of bright solitons and stationary vortex dipoles and
quadrapoles are identified and continued along the torus aspect ratio and along the frequency
parameter of the solution. In this work the various localization and stability properties of
such solutions are detailed, and the windows of stability (and instability) for these solutions
are identified.