Accelerating Oscillatory Fronts in a Sonic Vacuum with Non- local Interactions

Abstract eng:
We describe a novel class of dynamical excitations -- accelerating oscillatory fronts in nonlinear sonic vacua with strongly non-local effects. Such models naturally arise in dynamics of common and popular lattices. In this study, we consider a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. The front propagation obeys the scaling law l ~ t 4/3 . This scaling law results from the nonlocal effects; we derive it analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initiate the front propagation. The initiation threshold is explained on the basis of a simplified discrete model, further reduced to a new completely integrable nonlinear system.

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