Dark Solitons in Acoustic Transmission Line Metamaterials

Abstract

We study dark solitons, namely density dips with a phase jump across the density minimum, in a one-dimensional, weakly lossy nonlinear acoustic metamaterial, composed of a waveguide featuring a periodic array of side holes. Relying on the electroacoustic analogy and the transmission line approach, we derive a lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. The latter, using the method of multiple scales, is reduced to a defocusing nonlinear Schrödinger equation, which leads to dark soliton solutions. The dissipative dynamics of these structures is studied via soliton perturbation theory. We investigate the role—and interplay between—nonlinearity, dispersion and dissipation on the soliton formation and dynamics. Our analytical predictions are corroborated by direct numerical simulations.