Dynamics of Rogue waves in one-dimensional acoustic transmission line metamaterials

Analytically, modulational instability phenomenon and Rogue wave propagation are studied in an acoustic metamaterial based on the one-dimensional transmission line approach. Kirchhoff’s pressure and volume velocity laws for two successive cells and the multiple scales method allowed the determination of coupled nonlinear Schrödinger equations. By applying the disturbance method in amplitude to the coupled nonlinear Schrödinger equations, the modulational instability gain is obtained, and its curves are plotted. The similarity technique combined with the first- and second-order rational solutions of the one-dimensional Manakov system, which serve as prototypes of rogue wavelike solutions, is used to illustrate the dynamics of Rogue waves in the proposed model. The role and interplay between nonlinearity, dispersion, and diffraction parameters are investigated on the modulational instability gain and formation of Rogue waves. The results indicate that the modulational instability gain and Rogue wave intensities depend on the radius, thickness, and distance between the two plates of the proposed acoustic metamaterial model. To design such metamaterials, these parameters can be considered to minimize the damage caused by the dynamics of Rogue waves. The present results are innovative and have interesting applications in the engineering sciences.