Long time motion of NLS solitary waves in a confining potential

Details Long time motion of NLS solitary waves in a confining potential Long time motion of NLS solitary waves in a confining potential

2005-03-07

arxiv.org/abs/math-ph/0503009v1

Annales Henri Poincare, 7(4), pages 621--660, 2006.

Physics

Mathematical Physics

42 pages, 2 figures

Scientific paper

10.1007/s00023-006-0263-y

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger 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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