05-92 B.L.G. Jonsson, J. Froehlich, S. Gustafson, I.M. Sigal

Long Time Motion of NLS Solitary Waves in a Confining Potential (693K, PDF) Mar 7, 05

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Abstract. We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schr\"odinger 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.

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