Simple Non Linear Klein-Gordon Equations in 2 space dimensions, with long range scattering

Abstract

We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that the modified wave operators can be chosen such that they linearize the non-linear representation of the Poincaré group defined by the NLKG.

19 pages, LaTeX, To appear in Lett. Math. Phys

References in corpus (2)

• A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation
• Long Range Scattering and Modified Wave Operators for the Maxwell-Schr"odinger system I.The case of vanishing asymptotic magnetic field