Soliton interaction and nonlinear localized waves in one-dimensional nonlinear acoustic metamaterials

Abstract

In this study, we investigate soliton interactions and localized wave phenomena in nonlinear acoustic metamaterials with coupling coefficients. By employing the Lindstedt-Poincaré perturbation method and a multi-scale analysis, we derive the dispersion relation for the nonlinear Schrödinger equation. The dispersion curve reveals two propagation modes: the acoustic mode and the optical mode. Particular emphasis is placed on the dynamics of bright solitons in both low- and high-frequency bands, as well as energy propagation within the forbidden bandgap. Notably, soliton pairs emerge in the allowed phonon bands, illustrating their interaction characteristics. In the forbidden bandgap, we demonstrate that when the driving amplitude exceeds the supratransmission threshold, a train of pulses forms, leading to the generation of a dark soliton. These findings are supported by full numerical simulations of the nonlinear discrete coupled diatomic chain model. Furthermore, the modified model introduces novel features, making it a promising framework for exploring delocalized wave phenomena in future study.