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

Jun Ichi Segata

doi:10.1080/03605302.2014.930753

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

Jun Ichi Segata

Research output: Contribution to journal › Article › peer-review

12 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 language	English
Pages (from-to)	309-328
Number of pages	20
Journal	Communications in Partial Differential Equations
Volume	40
Issue number	2
DOIs	https://doi.org/10.1080/03605302.2014.930753
Publication status	Published - Feb 1 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/03605302.2014.930753

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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}",

note = "Funding Information: The author is partially supported by MEXT, Grant-in-Aid for Young Scientists (A) 25707004 and Grant for the Sumitomo Foundation, Basic Science Research Projects 120043. Publisher Copyright: {\textcopyright} 2015, Taylor & Francis Group, LLC.",

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N2 - 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.

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

Abstract

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