Interaction of localized solutions for subcritical bifurcations

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Abstract
We discuss the interaction of localized solutions as they arise for the subcritical bifurcation to traveling waves. We find that for a large parameter range the localized solutions can interact so that they emerge after the collision with a size and shape unchanged compared to that well before the collision. The mechanism for this behavior, which is unusual for a strongly dissipative system, is qualitatively different from that associated with solitons for completely integrable systems. In accord with this we find that for other parameter values counterpropagating localized solutions can annihilate.