Spatiotemporal Complexity in Traveling Patterns

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Abstract
This is a study of the nonlinear interactions of solitary waves or impulses in homogeneous, extended media. We obtain the set of ordinary differential equations for the positions of the impulses in the nearest-neighbor approximation. Solutions with constant velocity lead to pattern maps that give the successive spacings of the impulses. From among the infinitely many metastable patterns given by the maps, the system chooses one asymptotically through a hierarchical evolution.

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