Geodesic
Blowup/scattering alternative for a~discrete family of static critical solutions with various number of unstable eigenmodes
Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 119-144

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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.
Keywords: nonlinear wave equations, blowup solutions, self-similar solutions. 
@article{MM_2010_22_8_a9,
     author = {Evgeny E. Donets and Edik A. Hayryan and Oksana I. Streltsova},
     title = {Blowup/scattering alternative for a~discrete family of static critical solutions with various number of unstable eigenmodes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {119--144},
     publisher = {mathdoc},
     volume = {22},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_8_a9/}
}
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Evgeny E. Donets; Edik A. Hayryan; Oksana I. Streltsova. Blowup/scattering alternative for a~discrete family of static critical solutions with various number of unstable eigenmodes. Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 119-144. http://geodesic.mathdoc.fr/item/MM_2010_22_8_a9/