07-229 W.K. Abou Salem

Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations (405K, Postscript) Oct 2, 07

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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.

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