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

Evgeny E. Donets ; Edik A. Hayryan ; Oksana I. Streltsova

Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 119-144.

Résumé

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.

Détail

Keywords: nonlinear wave equations, blowup solutions, self-similar solutions.

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