### Abstract

We consider the scattering problem for the Hartree type equation in ℝ^{n} with n≧2: {Mathematical expression} where {Mathematical expression} and * denotes the convolution in ℝ^{n}. We prove the existence of wave operators in H^{0, k} = {ψ∈L^{2}(ℝ^{n});|x|^{kψ∈}L^{2}(ℝ^{n})} for any positive integer k under the assumption 1<γ_{1}, γ_{2}<2. This is an optimal result in the sense that the existence of wave operators breaks down if min (γ_{1}, γ_{2}≢1. The case where 1<γ_{1}, γ_{2} = 2 is also treated according to the sign of λ_{2}.

Original language | English |
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Pages (from-to) | 259-275 |

Number of pages | 17 |

Journal | Communications in Mathematical Physics |

Volume | 146 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1992 May 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Nawa, H., & Ozawa, T. (1992). Nonlinear scattering with nonlocal interaction.

*Communications in Mathematical Physics*,*146*(2), 259-275. https://doi.org/10.1007/BF02102628