Soliton interaction with slowly varying potentials

Details Soliton interaction with slowly varying potentials Soliton interaction with slowly varying potentials

2007-09-04

arxiv.org/abs/0709.0478v2

Mathematics

Analysis of PDEs

Scientific paper

We study the Gross-Pitaevskii equation with a slowly varying smooth potential, $V(x) = W(hx)$. We show that up to time $\log(1/h)/h $ and errors of size $h^2$ in $H^1$, the solution is a soliton evolving according to the classical dynamics of a natural effective Hamiltonian, $ (\xi^2 + \sech^2 * V (x))/2 $. This provides an improvement ($ h \to h^2 $) compared to previous works, and is strikingly confirmed by numerical simulations.

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