# Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials

## TL;DR

This paper analytically and numerically investigates bright and gap solitons in a nonlinear acoustic metamaterial composed of an air-filled waveguide with elastic plates, deriving models and solutions that reveal their dynamics and dissipation effects.

## Contribution

It introduces a nonlinear lattice model for membrane-type acoustic metamaterials and derives analytical solutions for bright and gap solitons, including effects of dissipation.

## Key findings

- Analytical expressions for bright and gap solitons were obtained.
- Numerical simulations confirmed the dissipation-induced dynamics of solitons.
- Good agreement between analytical and numerical results was observed.

## 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 Schr\"odinger 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.