@article{8d1ba8fbff6d4dfa936f734b0894a77a,
title = "Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions",
abstract = "In this paper, we consider the long time behavior of the solution to the quadratic nonlinear Klein–Gordon equation (NLKG) in two space dimensions: (Formula Presented), where □ = ∂t 2 − Δ is d{\textquoteright}Alembertian. For a given asymptotic profile uap, we construct a solution u to (NLKG) which converges to uap as t → ∞. Here the asymptotic profile uap 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.",
author = "Satoshi Masaki and Segata, {Jun Ichi}",
note = "Funding Information: Received by the editors November 25, 2016, and, in revised form, April 17, 2017. 2010 Mathematics Subject Classification. Primary 35L71; Secondary 35B40, 81Q05. Key words and phrases. Scattering problem. The first author was partially supported by the Sumitomo Foundation, Basic Science Research Projects No. 161145. The second author was partially supported by JSPS, Grant-in-Aid for Young Scientists (A) 25707004. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2018",
doi = "10.1090/tran/7262",
language = "English",
volume = "370",
pages = "8155--8170",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "11",
}