Modulational instability and rogue waves in one-dimensional nonlinear acoustic metamaterials: case of diatomic model

Abstract

In this paper, by means of the expanded Taylor series and Lindstedt-Poincar ́e perturbation methods, the coupled nonlinear Schrödinger equations (CNLSE) modeling the propagation of acoustic waves in acoustic metamaterial is obtained. Using these equations, the Modulational Instability (MI) phenomenon is observed in disturbance mode. Manakov integrable system is derived with suitable parameters and we shown that the Rogue Waves (RWs) can propagate diatomic acoustic metamaterials.

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

“…where a, b, c, d are the real contants. We study the stability of these plane wave solutions by introducing a slight perturbation in their amplitudes as [12,41]…”

“…They are relatively large, and spontaneous waves and their appearance may result in catastrophic damage [10]. Their basic characteristics are large amplitude, unexpected, coming out from nowhere without warning, and suddenly vanishing without trace [11,12].…”

“…Rogue wave generation is related to modulation instability (MI) [8,12,13]. The interplay between the dispersion, diffraction, and nonlinear effects can result in MI.…”

“…The interplay between the dispersion, diffraction, and nonlinear effects can result in MI. This is a universal and important physical phenomenon [12]. Research on MI is conducive to improving the performance of optical communication system [8].…”

“…Recent studies have been conducted on the solutions of nonlinear wave theory [21][22][23][24]. The nonlinear Schrödinger (NLS) equation has extensive physical applications in nonlinear optics [25], acoustics [7,12], plasma [26] and water waves [27]. Peregrine [28] gave the analytical expression of Rogue waves in the first-order as a result of MI on a constant wave background.…”