On convergence towards a self-similar solution for a nonlinear wave equation - a case study
arXiv:math-ph/0412038 · doi:10.1103/PhysRevD.72.045013
Abstract
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.
9 pages, 5 figures