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A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation. (English) Zbl 1106.35072

Summary: 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.

MSC:

35Q40 PDEs in connection with quantum mechanics
35L15 Initial value problems for second-order hyperbolic equations
74J30 Nonlinear waves in solid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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