We prove existence of a countable family of spherically symmetric self-similar wave maps from the Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state… (More)

We show that the (4 + 1)-dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere… (More)

We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) space by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with… (More)

We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a… (More)

In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity utt−∆u = u in three space dimensions. We show that for… (More)

A brief review of recent research on soliton and black hole solutions of Einstein’s equations with nonlinear field sources is presented and some open questions are pointed out.

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral… (More)

It is shown that Einstein-Yang-Mills-dilaton theory has a countable family of static globally regular solutions which are purely magnetic but uncharged. The discrete spectrum of masses of these… (More)

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar… (More)

We present a detailed analytical study of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using a shooting argument we prove that there is a countable family… (More)