# Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions

Satoshi Masaki, Jun ichi Segata, Kota Uriya

1 被引用数 (Scopus)

## 抄録

In this paper, we study large time behavior of complex-valued solutions to nonlinear Klein-Gordon equation with a gauge invariant quadratic nonlinearity in two spatial dimensions. To find a possible asymptotic behavior, we consider the final value problem. It turns out that one possible behavior is a linear solution with a logarithmic phase correction as in the real-valued case. However, the shape of the logarithmic correction term has one more parameter which is also given by the final data. In the real case the parameter is constant so one cannot see its effect. However, in the complex case it varies in general. The one dimensional case is also discussed.

本文言語 英語 177-203 27 Journal des Mathematiques Pures et Appliquees 139 https://doi.org/10.1016/j.matpur.2020.03.009 出版済み - 7月 2020

• 数学 (全般)
• 応用数学

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