### Abstract

We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical power p=1+2/n in space dimensions n=2 and 3 and for the Hartree equation with potential |x|^{-1} in space dimension n≥2. We prove the existence of modified wave operators in the L^{2} sense on a dense set of small and sufficiently regular asymptotic states.

Original language | English |
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Pages (from-to) | 619-645 |

Number of pages | 27 |

Journal | Communications in Mathematical Physics |

Volume | 151 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1993 Feb |

Externally published | Yes |

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### ASJC Scopus subject areas

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