Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of theamplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. Weexamine this process for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at the other.The supratransmission regime occurs for driving frequencies above the upper band edge and originates fromdirect moving discrete breather creation. We derive approximate analytical estimates of the supratransmissionthreshold, which are in excellent agreement with numerics. When analyzing the long-time behavior, we discoverthat, below the supratransmission threshold, a conducting stationary state coexists with the insulatingone. We explain the bistable nature of the energy flux in terms of the excitation of quasiharmonic extendedwaves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonableagreement with numerical experiments.