Propagation of acoustic solitons in a nonlinear left-handed transmission line

We study analytically and numerically acoustic soliton propagation in a nonlinear left-handed transmission line with nonlinear elements that incorporate Helmholtz resonators. We propose a theoretical model of the system integrating acoustic compliance with nonlinear effects, which relies on a transmission-line approach. Importantly, by means of a semi-discrete approximation, we can derive a nonlinear Schrödinger equation and thus show that the system supports both bright and dark acoustic solitons depending on the choice of carrier frequency. The values of the Helmholtz resonators parameters strongly influence the frequency bands, the stability of the waves, as well as their propagation. We perform systematic numerical simulations of the Nonlinear Schrödinger equation (NLSE) to show the spectral stability/instability of the initial waves. We then demonstrate that the nonlinear discrete lattice model can support the propagation of the solitons borrowed from the NLSE. Our findings suggest that the predicted structures are quite robust and the acoustic solitons persists throughout long simulation times.