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Acoustic solitons in waveguides with Helmholtz resonators: Transmission line approach

V. Achilleos1, O. Richoux2, G. Theocharis2, and D. J. Frantzeskakis1

  • 1Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
  • 2LUNAM Université, Université du Maine, CNRS, LAUM UMR 6613, Av. O. Messiaen, 72085 Le Mans, France

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Phys. Rev. E 91, 023204 – Published 13 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.023204

Abstract

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.

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Phys. Rev. E 91, 023204– Published 13 February, 2015
  • Received 2 September 2014
  • Revised 19 January 2015

©2015 American Physical Society

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