Soliton dynamics in a potential

J. C. Bronski, R. L. Jerrard

Research output: Contribution to journalArticlepeer-review

Abstract

We study the semiclassical limit of subcritical focussing NLS with a potential, for initial data of the form s(cursive Greek chi-cursive Greek chi0/∈)ei v0-cursive Greek chi/∈, 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(cursive Greek chi-cursive Greek chi∈(t)/∈)ei v∈(t)-cursive Greek chi/∈, and we show that the approximate center of mass cursive Greek chi(·) converges to a solution of the equation cursive Greek chi″ = -DV(cursive Greek chi), cursive Greek chi(0) = cursive Greek chi0, cursive Greek chi′(0) = v0 as ∈ → 0.

Original languageEnglish (US)
Pages (from-to)329-342
Number of pages14
JournalMathematical Research Letters
Volume7
Issue number2-3
DOIs
StatePublished - 2000

ASJC Scopus subject areas

  • Mathematics(all)

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