Stability of small solitary waves for the one-dimensional nls with an attractive delta potential

Satoshi Masaki; Jason Murphy; Jun Ichi Segata

doi:10.2140/apde.2020.13.1099

Stability of small solitary waves for the one-dimensional nls with an attractive delta potential

Satoshi Masaki, Jason Murphy, Jun Ichi Segata

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

6 Citations (Scopus)

Abstract

We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t →∞. In particular, we establish the asymptotic stability of the family of small solitary waves.

Original language	English
Pages (from-to)	1099-1128
Number of pages	30
Journal	Analysis and PDE
Volume	13
Issue number	4
DOIs	https://doi.org/10.2140/apde.2020.13.1099
Publication status	Published - 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2020.13.1099

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title = "Stability of small solitary waves for the one-dimensional nls with an attractive delta potential",

abstract = "We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t →∞. In particular, we establish the asymptotic stability of the family of small solitary waves.",

author = "Satoshi Masaki and Jason Murphy and Segata, {Jun Ichi}",

note = "Funding Information: Masaki was supported by JSPS KAKENHI, grant numbers 17K14219, 17H02854, and 17H02851. Segata is partially supported by JSPS KAKENHI, grant number 17H02851. We are grateful to T. Inui for pointing out an error in the original proof of Proposition 2.3, as well as to the anonymous referee for helpful comments. Publisher Copyright: {\textcopyright}2020 Mathematical Sciences Publishers.",

year = "2020",

doi = "10.2140/apde.2020.13.1099",

language = "English",

volume = "13",

pages = "1099--1128",

journal = "Analysis and PDE",

issn = "2157-5045",

publisher = "Mathematical Sciences Publishers",

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TY - JOUR

T1 - Stability of small solitary waves for the one-dimensional nls with an attractive delta potential

AU - Masaki, Satoshi

AU - Murphy, Jason

AU - Segata, Jun Ichi

N1 - Funding Information: Masaki was supported by JSPS KAKENHI, grant numbers 17K14219, 17H02854, and 17H02851. Segata is partially supported by JSPS KAKENHI, grant number 17H02851. We are grateful to T. Inui for pointing out an error in the original proof of Proposition 2.3, as well as to the anonymous referee for helpful comments. Publisher Copyright: ©2020 Mathematical Sciences Publishers.

PY - 2020

Y1 - 2020

N2 - We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t →∞. In particular, we establish the asymptotic stability of the family of small solitary waves.

AB - We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t →∞. In particular, we establish the asymptotic stability of the family of small solitary waves.

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DO - 10.2140/apde.2020.13.1099

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SN - 2157-5045

VL - 13

SP - 1099

EP - 1128

JO - Analysis and PDE

JF - Analysis and PDE

IS - 4

ER -

Stability of small solitary waves for the one-dimensional nls with an attractive delta potential

Abstract

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