Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential

Scipio Cuccagna, Nicola Visciglia, Vladimir Georgiev

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We prove decay and scattering of solutions of the nonlinear Schrödinger equation (NLS) in ℝ with pure power nonlinearity with exponent 3<p<5 when the initial datum is small in Σ (bounded energy and variance) in the presence of a linear inhomogeneity represented by a linear potential that is a real-valued Schwarz function. We assume absence of discrete modes. The proof is analogous to the one for the translation-invariant equation. In particular, we find appropriate operators commuting with the linearization.

Original languageEnglish
Pages (from-to)957-981
Number of pages25
JournalCommunications on Pure and Applied Mathematics
Volume67
Issue number6
DOIs
Publication statusPublished - 2014 Jun
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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