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Interaction Manifolds for Reaction Diffusion Equations in Two Dimensions

2010
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SIAM Journal on Applied Dynamical Systems
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We consider a general planar reaction diffusion equation which we hypothesize has a localized traveling wave solution. Under assumptions which are no stronger than those needed to prove the stability of a single pulse, we prove that the PDE has solutions which are roughly the linear superposition of two pulses, so long as they move along trajectories which are not parallel. In particular, we prove that if the initial data for the equation is close to the sum of two separated pulses, then the

doi:10.1137/090770692
fatcat:tigfznglmfdczlwjrj72gbgrgm