Blowup/scattering alternative for a discrete family of static critical solutions with various number of unstable eigenmodes

Decay of regular static spherically symmetric solutions in the SU(2) Yang-Mills-dilaton (YMd) system of equations under the independent excitation of their unstable eigenmodes has been studied self-consistently in the nonlinear regime. We have obtained strong numerical evidences that all static YMd solutions are distinct local threshold configurations, separating blowup and scat-tering solutions and the main unstable eigenmodes are only those responsible for the blowup/scattering alternative. On the other hand excitation of higher unstable eigenmodes always leads to finite-time blowup. The decay of the lowest $N=1$ static YMd solution is an exceptional case because the resulting waves reveal features peculiar to solitons.