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

Satoshi Masaki, Jun ichi Segata, Kota Uriya

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)177-203
Number of pages27
JournalJournal des Mathematiques Pures et Appliquees
Volume139
DOIs
Publication statusPublished - Jul 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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