Phononic Rogue Waves

Abstract

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schroedinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue wave like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.

9 pages, 4 figures

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• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• Capillary rogue waves
• Universal nature of the nonlinear stage of modulational instability
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Cited by in corpus (4)

• Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates
• Rogue and solitary waves in coupled phononic crystals
• Possible realization of a phononic tsunami in a wedge-shaped sample
• Edge Solitons in a Nonlinear Mechanical Topological Insulator