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Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions.
- Source :
-
Journal de Mathematiques Pures et Appliquees . Jul2020, Vol. 139, p177-203. 27p. - Publication Year :
- 2020
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *KLEIN-Gordon equation
*QUADRATIC equations
*NONLINEAR equations
Subjects
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 139
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 143617580
- Full Text :
- https://doi.org/10.1016/j.matpur.2020.03.009