Title: Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials,
Abstract: We study analytically and numerically envelope solitons (bright and gap
solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an
air-filled waveguide periodically loaded by clamped elastic plates. Based on
the transmission line approach, we derive a nonlinear dynamical lattice model
which, in the continuum approximation, leads to a nonlinear, dispersive and
dissipative wave equation. Applying the multiple scales perturbation method, we
derive an effective lossy nonlinear Schrödinger equation and obtain
analytical expressions for bright and gap solitons. We also perform direct
numerical simulations to study the dissipation-induced dynamics of the bright
and gap solitons. Numerical and analytical results, relying on the analytical
approximations and perturbation theory for solions, are found to be in good
agreement.