Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions
Analysis of PDEs
2017-04-28 v2
Abstract
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges to given asymptotic profile as t goes infinity. Here the asymptotic profile is given by the leading term of the solution to the linear Klein-Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on Fourier series expansion of the nonlinearity.
Cite
@article{arxiv.1612.00109,
title = {Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions},
author = {Satoshi Masaki and Jun-ichi Segata},
journal= {arXiv preprint arXiv:1612.00109},
year = {2017}
}
Comments
16 pages