Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications
2012
Session Number:B4L-A
Session:
Number:470
Breathers and surface modes in oscillator chains with Hertzian interactions
Guillaume James, Jesús Cuevas, Panayotis G. Kevrekidis,
pp.470-473
Publication Date:
Online ISSN:2188-5079
[1] N. Boechler, G. Theocharis and C. Daraio. Bifurcation-based acoustic switching and rectification, Nat. Mater. 10 (2011), 665-668.
[2] N. Boechler, G. Theocharis, S. Job, P.G. Kevrekidis, M.A. Porter and C. Daraio. Discrete breathers in one-dimensional diatomic granular crystals, Phys. Rev. Lett. 104 (2010), 244302.
[3] S. Flach and A. Gorbach. Discrete breathers : advances in theory and applications, Phys. Rep. 467 (2008), 1-116.
[4] G. James. Nonlinear waves in Newton's cradle and the discrete p-Schrödinger equation, Math. Models Meth. Appl. Sci. 21 (2011), 2335-2377.
[5] G. James, P.G. Kevrekidis and J.Cuevas. Breathers in oscillator chains with Hertzian interactions (2011), arXiv:1111.1857v1 [nlin.PS]. Submitted to Physica D.
[6] R.S. MacKay and S. Aubry. Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity 7 (1994), 1623-1643.
[7] V.F. Nesterenko, Dynamics of heterogeneous materials, Springer Verlag, 2001.
[8] N.-S. Nguyen and B. Brogliato. Shock dynamics in granular chains: numerical simulations and comparison with experimental tests, Granular Matter 14 (2012), 341-362.
[9] J.-A. Sepulchre and R.S. MacKay. Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators, Nonlinearity 10 (1997), 679-713.
[10] Y. Starosvetsky, M. Arif Hasan, A.F. Vakakis and L.I. Manevitch. Strongly nonlinear beat phenomena and energy exchanges in weakly coupled granular chains on elastic foundations, SIAM J. Appl. Math. 72 (2012), 337-361.
[11] Y. Starosvetsky, K. R. Jayaprakash and A.F. Vakakis. Scattering of solitary waves and excitation of transient breathers in granular media by light intruders, J. Appl. Mech. 79 (2012), 011001.
[12] A. Stefanov and P.G. Kevrekidis. On the existence of solitary traveling waves for generalized Hertzian chains, J. Nonlinear Sci. 22 (2012), 327-349.
[13] G. Theocharis, N. Boechler, P. G. Kevrekidis, S. Job, M.A. Porter, and C. Daraio. Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals, Phys. Rev. E. 82 (2010), 056604.