Coherent structures in nonlocally coupled systems
Professor Arnd Scheel
School of Mathematics
University of Minnesota
Abstract: I will present an overview of recent efforts to characterize differences and similarities between locally and nonlocally coupled systems, focusing on the dynamics of coherent structures such as fronts and pulses. The first part of the talk will highlight similarities in the case of smooth structures, and show how "pointwise" spatial dynamics techniques such as center manifolds, Hamiltonian identities, or geometric singular perturbation theory can be adapted as tools to study systems with nonlocal coupling through smooth convolution kernels. The second part will illustrate differences that arise when solutions are not smooth, in the example of depinning transitions.
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