Long time motion of NLS solitary waves in a confining potential

• We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schrodinger equations with a confining, slowly varying external potential, V(x). A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential V(x) over a long time interval.

Nyckelord

nonlinear schrodinger-equations

scalar field-equations

asymptotic stability

ground-states

nontopological solitons

nonintegrable equations

dissipative systems

energy propagation

smoothing property

hartree equation

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