Final State Problem for the Cubic Nonlinear Schrödinger Equation with Repulsive Delta Potential

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4 Citations (Scopus)

Abstract

We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schrödinger equation with repulsive delta potential (δ-NLS). We shall prove that for a given small asymptotic profile u ap, there exists a solution u to (δ-NLS) which converges to u apin L 2(ℝ) as t → ∞. To show this result we exploit the distorted Fourier transform associated to the Schrödinger equation with delta potential.

Original languageEnglish
Pages (from-to)309-328
Number of pages20
JournalCommunications in Partial Differential Equations
Volume40
Issue number2
DOIs
Publication statusPublished - Feb 1 2015
Externally publishedYes

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Asymptotic Profile
Cubic equation
Nonlinear equations
Fourier transform
Fourier transforms
Nonlinear Equations
Asymptotic Behavior
Converge

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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title = "Final State Problem for the Cubic Nonlinear Schr{\"o}dinger Equation with Repulsive Delta Potential",
abstract = "We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schr{\"o}dinger equation with repulsive delta potential (δ-NLS). We shall prove that for a given small asymptotic profile u ap, there exists a solution u to (δ-NLS) which converges to u apin L 2(ℝ) as t → ∞. To show this result we exploit the distorted Fourier transform associated to the Schr{\"o}dinger equation with delta potential.",
author = "Segata, {Jun Ichi}",
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AB - We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schrödinger equation with repulsive delta potential (δ-NLS). We shall prove that for a given small asymptotic profile u ap, there exists a solution u to (δ-NLS) which converges to u apin L 2(ℝ) as t → ∞. To show this result we exploit the distorted Fourier transform associated to the Schrödinger equation with delta potential.

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