Localized Structures in Dissipative Nonlinear Systems - Abstract
Wolfrum, Matthias
We investigate the time evolution of pulse solutions of the Schnakenberg model under the assumption that one of the diffusion parameters is small. Semi-strong pulse interaction means, that the species with the short diffusion length displays sharp pulses that show a slow motion caused by an interaction through the nonhomogeneos profile displayed by the other species between the pulses. In particular, we show that there exist two fundamentally different mechanisms of semi-strong pulse interaction, depending on the scaling assumptions for the parameters. For both cases, we give an asymptotic description of the pulse profiles and pulse motion due to interaction. We study in detail the behavior of solutions with one or two pulses and discuss some fundamental qualitative differences between the two interaction mechanisms.