Impact of viscothermal loss on modulation instability and rogue waves in left-handed nonlinear diffractive acoustic transmission line metamaterials

Abstract

In this study, the transmission line approach is used to describe the studied acoustic metamaterial model. Through Kirchoff’s pressure and volume-velocity laws and using multiple scales method, nonlinear coupled Schrödinger equations are obtained. Then, the amplitude disturbance method is applied to these equations to obtain and plot the modulational instability gain curves. Analytically, the impact of viscothermal loss on the modulational instability gain is studied. The similarity technique is used to derive integrable Manakov’s equations. First and second-order rational rogue wavelike solutions of coupled nonlinear Schrödinger are deduced. The results indicate that the modulational instability gain and Rogue wave intensities depend on the viscothermal parameter. This parameter can be considered in the design of nonlinear acoustic metamaterials to minimize the damage caused by the dynamics of freak waves.