Lindblad, Hans; Soffer, Avy A remark on long range scattering for the nonlinear Klein-Gordon equation. (English) Zbl 1080.35044 J. Hyperbolic Differ. Equ. 2, No. 1, 77-89 (2005). Summary: We consider the scattering problem for the nonlinear Klein-Gordon equation with long range nonlinearity in one dimension. We prove that for all prescribed asymptotic solutions there is a solution of the equation with such behavior, for some choice of initial data. In the case the nonlinearity has the good sign (repulsive) the result bold for arbitrary size asymptotic data. The method of proof is based on reducing the long range phase effects to an ordinary differential equation; this is done via an appropriate ansatz. We also find the complete asymptotic expansion of the solutions. Cited in 28 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations 35P25 Scattering theory for PDEs Keywords:complete asymptotic expansion PDFBibTeX XMLCite \textit{H. Lindblad} and \textit{A. Soffer}, J. Hyperbolic Differ. Equ. 2, No. 1, 77--89 (2005; Zbl 1080.35044) Full Text: DOI arXiv References: [1] Delort J.-M., Ann. Sci. École Norm. Sup. 34 pp 1– [2] Hörmander L., Lectures on Nonlinear Hyperbolic Differential Equations (1997) [3] DOI: 10.1002/cpa.3160450902 · Zbl 0840.35065 [4] DOI: 10.1016/S1631-073X(03)00231-0 · Zbl 1045.35101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.