University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Monday 12 February, 12:10-1:00pm
                          6183 Bahen Center      



SPEAKER:  Jeremy Marzuola (UC Berkeley)

TITLE:    Stable perturbations of a minimal mass soliton for a 
	  saturated NLSE in 3d.

ABSTRACT: A nonlinear Schr\"odinger equation with a saturated, focusing 
	  nonlinearity will have both orbitally stable and unstable 
	  soliton solutions.  In particular, we explore stable 
	  perturbations of "minimal mass" solitons that live precisely 
	  at the boundary of those solutions.  Previous works have shown 
	  that such solutions are in fact nonlinearly unstable.  In the 
	  spirit of the works of Schlag and Krieger-Schlag, we construct 
	  a stable class (manifold) of perturbations for the minimal 
	  mass soliton based on spectral projections and regularity 
	  assumptions.  Along the way, we discuss various numerical/ 
	  analytical techniques for verifying the existence and 
	  properties of said solitons, as well as the spectral 
	  assumptions required.



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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
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