W.K. Abou Salem
Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations
(405K, Postscript)

ABSTRACT.  The effective long-time dynamics of solitary wave solutions of the 
nonlinear Schr?odinger equation in the presence of rough nonlinear perturba- 
tions is rigorously studied. It is shown that, if the initial state is close to a 
slowly travelling soliton of the unperturbed NLS equation (in $H^ 1$ norm), 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.