### Abstract

We study the global Cauchy problem for the non gauge invariant Schrödinger equations (Formula Presented). The application of the Galilei generator for the proof of the analytic smoothing effect of solutions to the Cauchy problem for non gauge invariant Schrödinger equations involves diffculties. In this paper we construct analytic solutions to the non gauge invariant Schrödinger equations in the case of analytic and suffciently small initial data. We use the power like analytic spaces and the analytic Hardy spaces as auxiliary analytic spaces characterized by the Galilei generator. Also we show that if the initial data ϕ decay exponentially and are suffciently small in an appropriate norm, then the solutions of the Cauchy problem for non gauge invariant Schrödinger equations exist globally in time and are analytic.

Original language | English |
---|---|

Pages (from-to) | 65-75 |

Number of pages | 11 |

Journal | Funkcialaj Ekvacioj |

Volume | 60 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 |

### Fingerprint

### Keywords

- Analytic smoothing effect
- Analytic solutions
- Nonlinear Schrödinger equation

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Funkcialaj Ekvacioj*,

*60*(1), 65-75. https://doi.org/10.1619/fesi.60.77

**Analyticity of solutions to the non gauge invariant Schrödinger equations.** / Hoshino, Gaku; Naumkin, Pavel I.

Research output: Contribution to journal › Article

*Funkcialaj Ekvacioj*, vol. 60, no. 1, pp. 65-75. https://doi.org/10.1619/fesi.60.77

}

TY - JOUR

T1 - Analyticity of solutions to the non gauge invariant Schrödinger equations

AU - Hoshino, Gaku

AU - Naumkin, Pavel I.

PY - 2017

Y1 - 2017

N2 - We study the global Cauchy problem for the non gauge invariant Schrödinger equations (Formula Presented). The application of the Galilei generator for the proof of the analytic smoothing effect of solutions to the Cauchy problem for non gauge invariant Schrödinger equations involves diffculties. In this paper we construct analytic solutions to the non gauge invariant Schrödinger equations in the case of analytic and suffciently small initial data. We use the power like analytic spaces and the analytic Hardy spaces as auxiliary analytic spaces characterized by the Galilei generator. Also we show that if the initial data ϕ decay exponentially and are suffciently small in an appropriate norm, then the solutions of the Cauchy problem for non gauge invariant Schrödinger equations exist globally in time and are analytic.

AB - We study the global Cauchy problem for the non gauge invariant Schrödinger equations (Formula Presented). The application of the Galilei generator for the proof of the analytic smoothing effect of solutions to the Cauchy problem for non gauge invariant Schrödinger equations involves diffculties. In this paper we construct analytic solutions to the non gauge invariant Schrödinger equations in the case of analytic and suffciently small initial data. We use the power like analytic spaces and the analytic Hardy spaces as auxiliary analytic spaces characterized by the Galilei generator. Also we show that if the initial data ϕ decay exponentially and are suffciently small in an appropriate norm, then the solutions of the Cauchy problem for non gauge invariant Schrödinger equations exist globally in time and are analytic.

KW - Analytic smoothing effect

KW - Analytic solutions

KW - Nonlinear Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85018329485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018329485&partnerID=8YFLogxK

U2 - 10.1619/fesi.60.77

DO - 10.1619/fesi.60.77

M3 - Article

VL - 60

SP - 65

EP - 75

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

SN - 0532-8721

IS - 1

ER -