Contents Online
Mathematical Research Letters
Volume 7 (2000)
Number 3
Soliton dynamics in a potential
Pages: 329 – 342
DOI: https://dx.doi.org/10.4310/MRL.2000.v7.n3.a7
Authors
Abstract
We study the semiclassical limit of subcritical focussing NLS with a potential, for initial data of the form $s(\frac{x-x_0}\epsilon) e^{i \frac{v_0\cdot x}\e}$, where $s$ is the ground state of an associated unscaled problem. We show that in the semiclassical limit, the solution has roughly the form $s(\frac{x-x^\epsilon(t)}\epsilon) e^{i \frac{v^\epsilon(t)\cdot x}\epsilon}$, and we show that the approximate center of mass $x^\e(\cdot)$ converges to a solution of the equation $x” = - DV(x), x(0) = x_0, x'(0) = v_0$ as $\epsilon\to 0$.
Published 1 January 2000