99-336 Jean Marie Linhart
Slow Blow Up in the (2+1)-dimensional $S^2$ Sigma Model (1537K, postscript) Sep 12, 99
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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.

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