An exact unstable mode of self-similar Yang--Mills solutionsin 5+1 dimensions
Piotr Bizoń
Abstract
Self-similar solutions play an important role in the formation of singularities in the Yang--Mills equations. In five space dimensions, these equations admit infinitely many self-similar solutions with an increasing number of unstable modes. It was observed numerically that all excited profiles share the least unstable eigenvalue λ=5. We explain this remarkable spectral property by an elementary construction of the corresponding eigenfunction in terms of the profile.
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