Discrete modulation instability and localized modes in chiral molecular chains with first- and third-neighbor interactions

In this paper, we examined the behavior of the modulated wave patterns and nonlinear supratransmission phenomenon in gyrotropy molecular chains where the first-neighbor and third-neighbor interactions are considered. We have established the propagation modes through the dispersion law showing two cutoff frequencies. Through the numerical simulation, we have depicted modulated waves, solitons interaction as well as the modulation instability growth rates brought by the variation of the third-neighbor interaction and effective mass. As it was predicted that the group velocities vanish at the carrier waves, we have uncoupled a system of the coupled nonlinear Schrödinger equation by neglecting the elastic interaction to drive one end of the chains. The driven amplitude generates the train of waves in the system. For a specific time of propagation, we have shown how the variation of driven amplitude can induce instability in the forbidden gap. The obtained results have opened new features to the train of pulses in gyrotropy molecular chains.