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Title: Breathers in a locally resonant granular chain with precompression

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computed exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.
 [1] ;  [2] ;  [3] ;  [1]
  1. Univ. of Pittsburgh, PA (United States)
  2. INRIA Grenoble-Rhone Alpes, Montbonnot-Saint-Martin (France)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0167-2789
Grant/Contract Number:
DMS-1007908; DMS-1506904; FA9550-12-1-0332; W911NF-15-1-0604; AC52-06NA25396
Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 331; Journal Issue: C; Journal ID: ISSN 0167-2789
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Mathematics; Material Science