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

TL;DR

This paper demonstrates long-range scattering for simple nonlinear Klein-Gordon equations in two dimensions, constructing modified wave operators that linearize the nonlinear Poincaré group representation.

Contribution

It introduces a method to construct modified wave operators for NLKG in 2D with mass resonance, enabling linearization of the nonlinear Poincaré group representation.

Findings

Solutions exhibit long-range scattering phenomena.

Modified wave operators are constructed and can linearize the nonlinear Poincaré group.

The approach advances understanding of scattering in low-dimensional nonlinear wave equations.

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 Poincar\'e group defined by the NLKG.