### 抄録

We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

元の言語 | English |
---|---|

ページ（範囲） | 4309-4328 |

ページ数 | 20 |

ジャーナル | Discrete and Continuous Dynamical Systems- Series A |

巻 | 37 |

発行部数 | 8 |

DOI | |

出版物ステータス | Published - 2017 8 1 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### これを引用

**Orbital stability and uniqueness of the ground state for the non-linear schrödinger equation in dimension one.** / Garrisi, Daniele; Gueorguiev, Vladimir Simeonov.

研究成果: Article

}

TY - JOUR

T1 - Orbital stability and uniqueness of the ground state for the non-linear schrödinger equation in dimension one

AU - Garrisi, Daniele

AU - Gueorguiev, Vladimir Simeonov

PY - 2017/8/1

Y1 - 2017/8/1

N2 - We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

AB - We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

KW - Schrödinger

KW - Stability

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85038121727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038121727&partnerID=8YFLogxK

U2 - 10.3934/dcds.2017184

DO - 10.3934/dcds.2017184

M3 - Article

AN - SCOPUS:85038121727

VL - 37

SP - 4309

EP - 4328

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 8

ER -