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An asymptotic equation of motion for the pattern interface in thedomain-forming reaction-diffusion systems is derived. The free boundary problemis reduced to the universal equation of non-local contour dynamics in twodimensions in the parameter region where a pattern is not far from the pointsof the transverse instabilities of its walls. The contour dynamics is studiednumerically for the reaction-diffusion system of the FitzHugh-Nagumo type. Itis shown that in the asymptotic limit the transverse instability of thelocalized domains leads to their splitting and formation of the multidomainpattern rather than fingering and formation of the labyrinthine pattern.Comment: 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys.  Rev.

Self-replication and splitting of domain patterns in reaction-diffusion systems with the fast inhibitor