Solitary wave dynamics in an external potential

• We study the behavior of solitary-wave solutions of some generalized nonlinear Schrodinger 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 consider 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.

Nyckelord

nonlinear schrodinger-equations

scalar field-equations

positive radial solutions

stability theory

nonintegrable equations

elliptic equation

hartree equation

ground-states

existence

uniqueness

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