English

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.

Keywords

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

R2 v1 2026-06-22T17:10:12.723Z