A Remark on Asymptotic Completeness for the Critical Nonlinear Klein-Gordon Equation |
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Authors: | Email author" target="_blank">Hans?LindbladEmail author Avy?Soffer |
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Institution: | (1) Department of Mathematics, University of California at San Diego, San Diego, CA, USA;(2) Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA |
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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.
Mathematics Subject Classifications (2000): 35L15, 74J30, 76B15 ★ Part of this work was done while H.L. was a Member of the
Institute for Advanced Study, Princeton, supported by the NSF grant DMS-0111298 to the Institute. H.L. was also partially
supported by the NSF Grant DMS-0200226. † Also a member of the Institute of Advanced Study, Princeton. Supported in part by
NSF grant DMS-0100490. |
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Keywords: | Klein-Gordon global existence long-range scattering and completeness |
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