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 piecewise linear nonlinearity, 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 discuss a quasicontinuum approximation of the FPU model that captures all three classes of the fronts and the relation between them. The talk is based on recent joint work with N. Gorbushin and L. Truskinovsky (ESPCI).