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Abstract: We study the collision of two fast solitons for the nonlinear Schr\-odingerequation in the presence of a spatially adiabatic external potential. For ahigh initial relative speed $\|v\|$ of the solitons, we show that, up to timesof order $\log\|v\|$ after the collision, the solitons preserve their shape in$L^2$-norm, and the dynamics of the centers of mass of the solitons isapproximately determined by the external potential, plus error terms due toradiation damping and the extended nature of the solitons. We remark on how toobtain longer time scales under stronger assumptions on the initial conditionand the external potential.



Author: W. K. Abou Salem, J. Froehlich, I. M. Sigal

Source: https://arxiv.org/



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