Walid K Abou Salem 2009 Nonlinearity 22 747 doi:10.1088/0951-7715/22/4/004
Walid K Abou Salem
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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.
37K55 Perturbations, KAM for infinite-dimensional systems
37K40 Soliton theory, asymptotic behavior of solutions
35Q51 Solitons (See also 37K40)
35Q55 NLS-like (nonlinear Schrödinger) equations (See also 37K10)
Issue 4 (April 2009)
Received 18 May 2008, in final form 22 January 2009
Published 26 February 2009
Walid K Abou Salem 2009 Nonlinearity 22 747
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