Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach

We report experimental results and study theoretically soliton formation and propagation in an airfilled acoustic waveguide side loaded with Helmholtz resonators. Our theoretical approach relies on a transmission-line description of this setting, which leads to a nonlinear dynamical lattice model. The latter is treated analytically, by means of dynamical systems and multiscale expansion techniques, and leads to various soliton solutions for the pressure. These include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons, as well as nonlinear Schr\"{o}odinger envelope solitons. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.