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We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations. [ABSTRACT FROM AUTHOR]

We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry-related spatial domains. Using experimental data, we verify this mapping with remarkable accuracy. For the performed experiment, we employ a construction technique based on local symmetries that allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains, and they clearly indicate that completely locally symmetric devices constitute a promising class of setups with regard to the manipulation of wave propagation. [ABSTRACT FROM AUTHOR]

We numerically investigate the dynamics of strongly disordered 1D lattices under single-particle displacements, using both the Hertzian model, describing a granular chain, and the α+β Fermi-Pasta-Ulam-Tsingou model (FPUT). The most profound difference between the two systems is the discontinuous nonlinearity of the granular chain appearing whenever neighboring particles are detached. We therefore sought to unravel the role of these discontinuities in the destruction of Anderson localization and their influence on the system's chaotic dynamics. Our results show that the dynamics of both models can be characterized by: (i) localization with no chaos; (ii) localization and chaos; (iii) spreading of energy, chaos, and equipartition. The discontinuous nonlinearity of the Hertzian model is found to trigger energy spreading at lower energies. More importantly, a transition from Anderson localization to energy equipartition is found for the Hertzian chain and is associated with the "propagation" of the discontinuous nonlinearity in the chain. On the contrary, the FPUT chain exhibits an alternate behavior between localized and delocalized chaotic behavior which is strongly dependent on the initial energy excitation. [ABSTRACT FROM AUTHOR]

Effective non-Hermitian Hamiltonians are obtained to describe coherent perfect absorbing and lasing boundary conditions. PT symmetry of the Hamiltonians enables us to design configurations which perfectly absorb at multiple frequencies. Broadened and flat perfect absorption is predicted at the exceptional point of PT-symmetry breaking while, for a particular case, absorption is enhanced with the use of gain. The aforementioned phenomena are illustrated for acoustic scattering through Helmholtz resonators revealing how tailoring the non-Hermiticity of acoustic metamaterials leads to novel mechanisms for enhanced absorption. [ABSTRACT FROM AUTHOR]

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.

This Letter presents the experimental characterization of nonreciprocal elastic wave transmission in a single-mode elastic waveguide. This asymmetric system is obtained by coupling a selection layer with a conversion layer: the selection component is provided by a phononic crystal, while the conversion is achieved by a nonlinear self-demodulation effect in a 3D unconsolidated granular medium. A quantitative experimental study of this acoustic rectifier indicates a high rectifying ratio, up to 10^{6}, with wide band (10 kHz) and an audible effect. Moreover, this system allows for wave-packet rectification and extends the future applications of asymmetric systems.

Nonlinear effects of acoustic wave propagation and dispersion are observed in a one-dimensional lattice made of Helmholtz resonators connected to a tube. These regularly spaced scatterers exhibit individually a wave frequency dependence, which induces a strong velocity dispersion. In addition, they exhibit a wave amplitude dependence (acoustic nonlinearity), which induces nonlinear effects on the dispersion relation of waves in the lattice. The usually observed forbidden frequency band gaps for the transmission coefficient through the lattice are shown to be amplitude dependent. Experimental results are compared to a developed model taking into account the nonlinear behavior of the Helmholtz resonator.

The propagation of transverse waves along a string loaded by masses, each of them being fixed to a spring with a quadratic nonlinearity, is studied. After presenting the nonlinear model and stating the equation of propagation into a lattice with discrete nonlinearities and disorder, we propose a perturbation approach to wave propagation in a nonlinear lattice using the Green's function formalism. We show how the nonlinearity acts on the propagation into a disordered lattice. In the low-frequency approximation, an analytical expression of the boundary between the propagative regime and the evanescent one is found. Numerical results are compared to the analytical results and phase diagrams are proposed in the ordered and disordered cases. A behavior of the transmission coefficient is found, on an empirical basis, as a function of the length of the lattice and the localization length in the nonlinear case. Finally, a dynamic approach is developed and the ordered and disordered cases are addressed. This method is based on a finite difference equation and allows the construction of the Poincaré section describing the propagation of the wave into the lattice. This approach distinguishes between the properties of propagation in the lattice in a propagative regime and in an evanescent one.