Soliton dynamics in a potential

  title={Soliton dynamics in a potential},
  author={Jared C. Bronski and Robert L. Jerrard},
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. 

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