Abstract. The effective long-time dynamics of solitary wave solutions of the nonlinear Schrödinger 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 H¹ norm), then, over a long time scale, the true solution of the initial value problem will be close to a soliton whose centre of mass dynamics is approximately determined by an effective potential that corresponds to the restriction of the nonlinear perturbation to the soliton manifold.

Print publication: Issue 4 (April 2009)
Received 18 May 2008, in final form 22 January 2009
Published 26 February 2009