Supratransmission phenomenon in a discrete electrical lattice with nonlinear dispersion

We introduce the driven Salerno equation describing the dynamics of modulated waves in a discrete nonlinear electrical transmission lattice submitted to a periodic driving source with constant amplitude. This equation admits only in the upper forbidden band gap a new analytical expression of the supratransmission threshold, BthrBthr, which depends on the nonlinear dispersion coefficient, μμ. BthrBthr increases (decreases) as μμ decreases (increases) and for the limit case where μμ vanishes, the value of BthrBthr is similar to that obtained in the cubic discrete nonlinear Schrödinger equation. Theoretical predictions of the supratrasmission phenomenon are confirmed by numerical simulations. We finally show that the driving amplitude must be slightly above the threshold to achieve a good supratransmission. Otherwise, the supratransmission takes place but the wave is destroyed.

► A new analytical expression of the threshold of supratransmission is calculated.
► Numerical simulation confirms analytical predictions.
► Higher values of driving amplitudes destroy wave transmission.