# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## On the real analyticity of the scattering operator for the Hartree equation

### Tom 95 / 2009

Annales Polonici Mathematici 95 (2009), 227-242 MSC: 35P25, 35Q55. DOI: 10.4064/ap95-3-3

#### Streszczenie

\def\barDelta{{\mit\Delta}}We study the real analyticity of the scattering operator for the Hartree equation $i\partial _tu=-{\mit\Delta} u+u(V*|u|^2)$. To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome dif{f}iculties which arise from absence of good properties as for the Klein–Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the nonlinear Klein–Gordon equation with cubic nonlinearity.

#### Autorzy

• Changxing MiaoInstitute of Applied Physics
and Computational Mathematics
P.O. Box 8009
Beijing, China, 100088
e-mail
of Engineering Physics
P.O. Box 2101
Beijing, China, 100088
and
School of Mathematics and Information Science
Henan Polytechnic University
Jiaozuo, China, 454000
e-mail