Soliton interaction with slowly varying potentials

Simple item page
dc.creatorHolmer, Justin
dc.creatorZworski, Maciej
dc.date2007-09-04
dc.date2007-09-24
dc.date.accessioned2026-07-07T08:31:18Z
dc.date.available2026-07-07T08:31:18Z
dc.descriptionWe 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, $ (ξ^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.
dc.identifierhttps://arxiv.org/abs/0709.0478
dc.identifierhttp://arxiv.org/abs/0709.0478
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138468
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleSoliton interaction with slowly varying potentials
dc.typetext

Files

Collections

arXiv