Abstract for Anna Vainchtein

Anna Vainchtein (University of Pittsburgh)

Friday, March 31, 2023
9:30-10:10am

Transition fronts and their universality classes

Abstract: Steadily moving transition fronts, bringing local transformation, symmetry breaking or collapse, are among the most important dynamic coherent structures. Nonlinear waves of this type play a major role in many modern applications involving the transmission of mechanical information in systems ranging from crystal lattices and metamaterials to civil engineering structures. While many different classes of such dynamic fronts are known, the relation between them remains obscure. In this talk I will consider a prototypical mechanical system, the FPU chain with bilinear interactions, and show that there are exactly three distinct classes of transition fronts, which differ fundamentally in how (and whether) they produce and transport oscillations. The availability of all three types of fronts as explicit solutions of the discrete problem enables identification of the exact mathematical origin of the particular features of each class. I will also present recent results on one type of transition waves, supersonic kinks, in problems with trilinear and fully nonlinear interactions. The talk is based on joint work with N. Gorbushin and L. Truskinovsky (ESPCI).