J. Frohlich, S. Gustafson, B. L. G. Jonsson, I. M. Sigal
Solitary wave dynamics in an external potential
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ABSTRACT. We study the behavior of solitary-wave solutions of some generalized
nonlinear Schr\"odinger equations with an external potential. The
equations have the feature that in the absence of the external potential,
they have solutions describing inertial motions of stable solitary waves.
We construct solutions of the equations with a non-vanishing external
potential corresponding to initial conditions close to one of these
solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton's equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping.