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Center for Nonlinear Studies |
Spatially localized structures are common in pattern forming systems, appearing in fluid mechanics, nonlinear optics, and chemical systems. These states often exhibit homoclinic snaking, a reference to the sequence of saddle-node bifurcations which connect localized structures of different widths. The most studied example is that which occurs in the Swift-Hohenberg equation, which is a canonical model for pattern formation. In this talk, I will use the Swift-Hohenberg equation to introduce homoclinic snaking in its simplest form. I will also show how variations of this same phenomenon occur in other simple PDEs. Finally, I will give several examples of homoclinic snaking in more realistic systems, including plane Couette flow.
Host: Golan Bel