University of Toronto
                  PDE/Applied Math/Analysis Seminar
                   Friday 19. October, 1:10-2:00pm
                          6183 Bahen Center



SPEAKER:  

Walid Abou-Salem (University of Toronto)

TITLE: 

Long-time dynamics of solitons in the presence of rough nonlinear 
perturbations

ABSTRACT: 

I discuss recent rigorous results on the effective long-time dynamics of 
solitary wave solutions of the nonlinear Schrodinger equation in the presence of 
rough nonlinear perturbations. Physically, nonlinear perturbations of NLS 
equations appear in 
Bose-Einstein experiments where the scattering length, which determines the 
nonlinear coefficient in the Gross-Pitaevskii equation, is modified using 
Feshbach resonances, such as in experiments involving atomic soliton 
lasers. It is shown that, if the initial state is close to a slowly 
travelling soliton of the unperturbed NLS equation, then, over a long time 
scale, the true solution of the initial value problem will be close to a 
soliton whose center of mass dynamics is approximately determined by an 
effective potential that corresponds to the restriction of the nonlinear 
perturbation to the soliton manifold. 



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