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

Scipio Cuccagna, Nicola Visciglia, Vladimir Simeonov Gueorguiev

Research output: Contribution to journal › Article

13 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
Externally publishedYes

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Small Solutions
Linearization
Nonlinear equations
Mathematical operators
Nonlinear Equations
Scattering
Decay
Inhomogeneity
Exponent
Nonlinearity
Invariant
Operator
Energy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential. / Cuccagna, Scipio; Visciglia, Nicola; Gueorguiev, Vladimir Simeonov.

In: Communications on Pure and Applied Mathematics, Vol. 67, No. 6, 2014, p. 957-981.

Research output: Contribution to journal › Article

Cuccagna, S, Visciglia, N & Gueorguiev, VS 2014, 'Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential' Communications on Pure and Applied Mathematics, vol. 67, no. 6, pp. 957-981. https://doi.org/10.1002/cpa.21465
Cuccagna S, Visciglia N, Gueorguiev VS. Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential. Communications on Pure and Applied Mathematics. 2014;67(6):957-981. https://doi.org/10.1002/cpa.21465
Cuccagna, Scipio ; Visciglia, Nicola ; Gueorguiev, Vladimir Simeonov. / Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential. In: Communications on Pure and Applied Mathematics. 2014 ; Vol. 67, No. 6. pp. 957-981.
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