### 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 _{ap}in 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 |
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Pages (from-to) | 309-328 |

Number of pages | 20 |

Journal | Communications in Partial Differential Equations |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1 2015 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

**Final State Problem for the Cubic Nonlinear Schrödinger Equation with Repulsive Delta Potential.** / Segata, Jun Ichi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Final State Problem for the Cubic Nonlinear Schrödinger Equation with Repulsive Delta Potential

AU - Segata, Jun Ichi

PY - 2015/2/1

Y1 - 2015/2/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84910121519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84910121519&partnerID=8YFLogxK

U2 - 10.1080/03605302.2014.930753

DO - 10.1080/03605302.2014.930753

M3 - Article

AN - SCOPUS:84910121519

VL - 40

SP - 309

EP - 328

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 2

ER -