Abstract.
We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schrödinger 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.
Communicated by Rafael D. Benguria
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Submitted: March 7, 2005 Accepted: January 9, 2006
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Jonsson, B.L.G., Fröhlich, J., Gustafson, S. et al. Long Time Motion of NLS Solitary Waves in a Confining Potential. Ann. Henri Poincaré 7, 621–660 (2006). https://doi.org/10.1007/s00023-006-0263-y
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DOI: https://doi.org/10.1007/s00023-006-0263-y