coherent structures

Tuesday, November 1, 2016 - 9:00am - 9:50am
Eduard-Wilhelm Kirr (University of Illinois at Urbana-Champaign)
I will discuss classical and recent results regarding asymptotic stability of solitary waves i.e., localized solutions of nonlinear wave equations propagating without changing shape. Begining with the work of Soffer and Weinstein in the ’90 we know that, under certain assumptions, solutions starting close to a solitary wave shadow nearby solitary waves before collapsing on one. The mathematical analysis relies on using dispersive estimates for the linearized dynamics at a fixed (rather arbitrarily chosen) solitary wave to control the nonlinearity.
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