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

Abstract

In this work, 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 Schodinger equations are obtained. Then, disturbance method in amplitude to these equations is applied to obtain and plot modulational instability gain curves. Analyticaly, the impact of viscothermal loss on modulational instability gain is studied. Similarity technique is used to find integrable Manakov’s equations. First and second-order rational rogue wavelike solutions of coupled nonlinear Schrodinger are obtained. The results indicate that the modulational instability gain and Rogue wave intensities can be depended on the
viscothermal parameter. This parameter can be considered to design nonlinear acoustic metamaterials, to minimize the damage caused by the dynamics of freak waves.

Generation and propagation of acoustic solitons in a periodic waveguide of air-water metamaterials

“…In this section, we present a TL based equivalent circuit to simulate the propagation of the soliton wave. This approach is widely used in linear acoustics [34,35] and nonlinear ultrasounds [36,37].…”