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. 
V. Achilleos, O. Richoux, G. Theocharis, and D. J. Frantzeskakis
nlin.PS cond-mat.mtrl-sci