## Abstract

We consider the 1D nonlinear Schrödinger equation with focusing point nonlinearity. "Point"means that the pure-power nonlinearity has an inhomogeneous potential and the potential is the delta function supported at the origin. This equation is used to model a Kerr-type medium with a narrow strip in the optic fibre. There are several mathematical studies on this equation and the local/global existence of a solution, blow-up occurrence, and blowup profile have been investigated. In this paper we focus on the asymptotic behavior of the global solution, i.e., we show that the global solution scatters as t → ±∞ in the L2 supercritical case. The main argument we use is due to Kenig-Merle, but it is required to make use of an appropriate function space (not Strichartz space) according to the smoothing properties of the associated integral equation.

Original language | English |
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Pages (from-to) | 35-60 |

Number of pages | 26 |

Journal | Transactions of the American Mathematical Society |

Volume | 374 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2020 |

## Keywords

- Nonlinear point interaction
- Scattering
- Schrödinger equation

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics