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We present some numerical findings concerning the nature of the blowup vs.global existence dichotomy for the focusing cubic nonlinear Klein-Gordonequation in three dimensions for radial data. The context of this study isprovided by the classical paper by Payne, Sattinger from 1975, as well as therecent work by K. Nakanishi, and the second author arXiv:1005.4894.Specifically, we numerically investigate the boundary of the forward scatteringregion. At this point we do not have sufficient numerical evidence that mightindicate whether or not the boundary remains a smooth manifold for generalenergies. In this updated version we include some fine-scale computations thatreveal more complicated structures than one might expect.

Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation