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Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. (English) Zbl 0979.35074

This paper concerns the existence of solutions consisting of two symmetric pulses moving apart from each other with slowly varying velocities. Critical maximum wave speeds are identified and ordinary differential equations are derived for the wave speed and for the separation distance between the pulses.

MSC:

35K57 Reaction-diffusion equations
35B25 Singular perturbations in context of PDEs
35B32 Bifurcations in context of PDEs
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
92E20 Classical flows, reactions, etc. in chemistry
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