Jean Marie Linhart
Slow Blow Up in the (2+1)-dimensional $S^2$ Sigma Model
(1537K, postscript)

ABSTRACT.  We study singularity formation in spherically symmetric solitons of
the charge one sector of the (2+1) dimensional $S^2$ sigma model, also
known as $\IC P^1$ wave maps, in the adiabatic limit.  These equations
are non-integrable, and so studies are performed numerically on
radially symmetric solutions using an iterative finite differencing
scheme.  Analytic estimates are made by using an effective Lagrangian
cutoff outside a ball of fixed radius.  We show the geodesic
approximation is valid when the cutoff is applied, with the cutoff
approaching infinity linearly as the reciprocal of the initial
velocity.  Additionally a characterization of the shape of a time
slice $f(r,T)$ with $T$ fixed is provided.