Highly Influenced

5 Excerpts

@inproceedings{Bronski2000SolitonDI, title={Soliton dynamics in a potential}, author={Jared C. Bronski and Robert L. Jerrard}, year={2000} }

- Published 2000
DOI:10.4310/MRL.2000.v7.n3.a7

We study the semiclassical limit of subcritical focussing NLS with a potential, for initial data of the form s(x−x0 )e v0·x , 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( x−x (t) )e v (t)·x , and we show that the approximate center of mass x (·) converges to a solution of the equation x′′ = −DV (x), x(0) = x0, x′(0) = v0 as → 0.