Solitary Wave Dynamics in an External Potential

Details Solitary Wave Dynamics in an External Potential Solitary Wave Dynamics in an External Potential

2003-09-23

arxiv.org/abs/math-ph/0309053v1

Comm. Math. Phys. 250(3) pp.613--642, 2004

Physics

Mathematical Physics

latex2e, 41 pages, 1 figure

Scientific paper

10.1007/s00220-004-1128-1

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.

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