Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations

Details Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations

2007-10-02

arxiv.org/abs/0710.0660v2

Physics

Mathematical Physics

Reference [16] added. 19 pages

Scientific paper

The effective long-time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in the presence of rough nonlinear perturbations 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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