Energy transmission in the forbidden band-gap of a nonlinear chain with global interactions

Abstract

The phenomenon of supratransmission in nonlinear systems with global interactions is predicted analytically for the first time. The model considered is a physically significant extension of the classical β-Fermi–Pasta–Ulam–Tsingou (β-FPUT) chain, with power-law interaction of degree α ⩾ 0. Using a relatively simple analytical theory, we derive the threshold that triggers the supratransmission process. The threshold for the short-range model is a particular case of our predictions. Our theoretical derivation shows that supratransmission is present for any power α > 1. We confirm numerically the validity of these results. Moreover, the numerical simulations also confirm the presence of supratransmission in the case of long-range interactions, in spite that the theoretical arguments are not valid for that case. It is worth pointing out that the present approach may be applied to other systems with global interactions.