  The boundary integral method is extended to derive closed
integro-differential equations applicable to computation of the shape and
propagation speed of a steadily moving spot and to the analysis of dynamic
instabilities in the sharp boundary limit. Expansion of the boundary integral
near the locus of traveling instability in a standard reaction-diffusion model
proves that the bifurcation is supercritical whenever the spot is stable to
splitting, so that propagating spots can be stabilized without introducing
additional long-range variables.
