### Abstract

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L^{2}(R) or in the Sobolev space H^{1}(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|^{2}u.

Original language | English |
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Pages (from-to) | 479-493 |

Number of pages | 15 |

Journal | Communications in Mathematical Physics |

Volume | 139 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1991 Aug |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

**Long range scattering for nonlinear Schrödinger equations in one space dimension.** / Ozawa, Tohru.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 139, no. 3, pp. 479-493. https://doi.org/10.1007/BF02101876

}

TY - JOUR

T1 - Long range scattering for nonlinear Schrödinger equations in one space dimension

AU - Ozawa, Tohru

PY - 1991/8

Y1 - 1991/8

N2 - We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

AB - We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

UR - http://www.scopus.com/inward/record.url?scp=0001366166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001366166&partnerID=8YFLogxK

U2 - 10.1007/BF02101876

DO - 10.1007/BF02101876

M3 - Article

AN - SCOPUS:0001366166

VL - 139

SP - 479

EP - 493

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -