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Letters in Mathematical Physics

, Volume 73, Issue 3, pp 249–258 | Cite as

A Remark on Asymptotic Completeness for the Critical Nonlinear Klein-Gordon Equation

  • Hans Lindblad
  • Avy Soffer
Article

Abstract

We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in hyperbolic coordinates to the study of an ODE. Similar arguments extend to higher dimensions and other long range type nonlinear problems.

Keywords

Klein-Gordon global existence long-range scattering and completeness 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at San DiegoSan DiegoUSA
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA

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