PHYSICAL MATHEMATICS SEMINAR
TOPIC: STABILITY OF PERIODIC SOLUTIONS OF THE
NONLINEAR SCHR\"ODINGER EQUATION
WITH ELLIPTIC FUNCTION POTENTIAL
SPEAKER: NATHAN KUTZ
Department of Applied Mathematics
University of Washington
Abstract:
We model a dilute gas Bose-Einstein condensate trapped in a standing light
wave by the cubic nonlinear Schr\"odinger equation with an elliptic
function potential. New families of stationary solutions are presented
and their stability is examined using analytic and numerical methods.
Jacobi elliptic Dn(x,k) solutions are found to be stable for defocusing,
whereas Jacobi elliptic Cn(x,k) solutions are found to be stable for
focusing. The linearized stability calculations allow us to generate a
set of criteria concerning the stability and instability of the various
families of solutions. Our results imply that for defocusing (repulsive
BEC), a large number of condensed atoms is sufficient to form a stable,
periodic condensate. For focusing (attractive BEC), solutions with nodes
are necessary.
DATE: TUESDAY, SEPTEMBER 26, 2000
TIME: 2:30 PM
LOCATION: Building 2, Room 338
Refreshments will be served at 3:30 PM in Building 2, Room 349.