A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation

Details A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation

2005-10-28

arxiv.org/abs/math/0510643v1

Mathematics

Analysis of PDEs

To appear in Lett. Math. Phys

Scientific paper

10.1007/s11005-005-0021-y

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.

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