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

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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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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