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Nonlocal Boundary Dynamics of Traveling Spots in a Reaction-Diffusion System

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.

preprint2000arXivOpen access
L. M. Pismen
nlin.PS
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L. M. Pismen

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