  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.
