On convergence towards a self-similar solution for a nonlinear wave equation - a case study

Details On convergence towards a self-similar solution for a nonlinear wave equation - a case study On convergence towards a self-similar solution for a nonlinear wave equation - a case study

2004-12-12

arxiv.org/abs/math-ph/0412038v1

Physics

Mathematical Physics

9 pages, 5 figures

Scientific paper

10.1103/PhysRevD.72.045013

We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate numerically that the resulting eigensystem provides an accurate description of the dynamics of convergence towards the attractor.

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