Mathematical Research Letters

Volume 7 (2000)

Number 3

Soliton dynamics in a potential

Pages: 329 – 342



J. C. Bronski

R. L. Jerrard


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 $\epsilon\to 0$.

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