Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

The propagation of the modulated wave (MW) pattern and its instability in the nonlinear medium is an important study from where experimental results are obtained. In this work, we use the nonlinear Schrodinger equation (NLSE) with saturation nonlinearity (SN) which describes the solitonic waves in the molecular chain (MC) model. We set our study on the effectiveness of the acoustic longitudinal velocity (ALV) which is related to the acoustic longitudinal vibration to investigate the behavior of the MW patterns as well as the modulation instability (MI) gain. Its results are that the ALV creates instability zones, increases MI bands, and shortens the transition regime of the MW pattern. For a long time of simulation and a great enough value of the ALV, the MWs feature chaos-like motion. Alongside these results the ALV obvious itself as a tool control of MWs as well as an energy source for the propagation of diverse MW-shaped in the MC.