Anti-localization of non-stationary quasi-waves in a strongly nonlinear $\beta$-FPUT chain

Abstract

Recently, a new general wave phenomenon, namely "the anti-localization of non-stationary linear waves", has been introduced and discussed (Shishkina et al., J. Sound. Vib. 553, 2023, 117673). This is zeroing of the propagating component for a non-stationary wave-field near a defect in infinitely long wave-guides. The phenomenon is known to be observed in both continuum and discrete mechanical systems with a defect, provided that the frequency spectrum for the corresponding homogeneous system possesses a stop-band. In this paper, we show that the anti-localization is also quite common for nonlinear systems. To demonstrate this, we numerically solve several non-stationary problems for an infinite strongly nonlinear $\beta$-FPUT chain with a defect. In our opinion, the anti-localization essentially influences the processes of heat transfer in linear and nonlinear lattices.