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

• Autorzy: Changxing Miao , Haigen Wu , Junyong Zhang
• Języki publikacji: EN

Abstrakty

EN

We study the real analyticity of the scattering operator for the Hartree equation $i∂_tu = -Δu + u(V*|u|²)$. To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties 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.

Kategorie tematyczne

• 35Q55: NLS-like equations (nonlinear Schr\"odinger)
• 35P25: Scattering theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2009
• Tom: 95
• Numer: 3
• Strony: 227-242

Daty

wydano

2009

Twórcy

autor

Changxing Miao

• Institute of Applied Physics, and Computational Mathematics, P.O. Box 8009, Beijing, China, 100088

autor

Haigen Wu

• The Graduate School of China Academy, of Engineering Physics, P.O. Box 2101, Beijing, China, 100088
• School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China, 454000

autor

Junyong Zhang

• The Graduate School of China Academy, of Engineering Physics, P.O. Box 2101, Beijing, China, 100088

Identyfikatory

DOI

10.4064/ap95-3-3