## The motion of weakly interacting pulses in reaction-diffusion systems.(English)Zbl 1007.35039

Author’s abstract: The interaction of stable pulse solutions on $$\mathbb{R}^1$$ is considered when distances between pulses are sufficiently large. We construct an attractive local invariant manifold giving the dynamics of interacting pulses in a mathematically rigorous way. The equations describing the flow on the manifold are also given in an explicit form. By it, we can easily analyze the movement of pulses such as repulsiveness, attractivity and/or the existence of bound states of pulses. Interaction of front solutions are also treated in a similar way.

### MSC:

 35K57 Reaction-diffusion equations 35B25 Singular perturbations in context of PDEs
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