Tuesday, March 19, 2013
316 Stanley Thomas Hall
Tulane University (Uptown)
Refreshments will be served
Roy Goodman, New Jersey Institute of Technology, Department of Mathematical Sciences
Complex low-dimensional dynamics in nonlinear wave dynamics
We consider low dimensional phenomena that occur in two systems whose macroscopic behavior is governed by the nonlinear Schrodinger equation. (1) The dynamics of light in small arrays of coupled waveguides, where certain assumptions are made on the spectrum of the potential (i.e. the waveguide) (2) the interaction of point vortices in a two-dimensional Bose-Einstein condensate. Both systems are well-modeled, over long times, by finite-dimensional Hamiltonian ODEs. We show that a wide array of bifurcations and behaviors are possible in these systems and that the systematic use of normal form analysis, computed using Lie transforms, makes discovering these phenomena possible.
Center for Computational Science, Stanley Thomas Hall 402, New Orleans, LA 70118 email@example.com