### Abstract

We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

Original language | English |
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Pages (from-to) | 397-410 |

Number of pages | 14 |

Journal | Reviews in Mathematical Physics |

Volume | 9 |

Issue number | 3 |

Publication status | Published - 1997 Apr |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Reviews in Mathematical Physics*,

*9*(3), 397-410.

**Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces.** / Nakamura, M.; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Reviews in Mathematical Physics*, vol. 9, no. 3, pp. 397-410.

}

TY - JOUR

T1 - Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces

AU - Nakamura, M.

AU - Ozawa, Tohru

PY - 1997/4

Y1 - 1997/4

N2 - We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

AB - We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

UR - http://www.scopus.com/inward/record.url?scp=0031285644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031285644&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 397

EP - 410

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 3

ER -