Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain

Abstract

We study numerically a discrete, nonlinear lattice, which is formed by a chain of pendula submitted to a harmonic-driving source with constant amplitude and parametrical excitation. A supratransmission phenomenon is obtained after the derivation of the homoclinic threshold for the case when the lattice is driven at one edge. The lattice traps gap solitons when the chain is subjected to a periodic horizontal displacement of the pivot. Discrete rogue waves are generated for the case when the pendulum is simultaneously driven and shaken. This work may pave the way for experimental generation of discrete rogue waves within simple devices.

Figures (9)

• Figure 1: Schematic representation of a pendulum chain connected by torsional springs subjected to a horizontal driving force. (a) front view; (b) profile view. Reproduced with permission from Ref. XuAlexanderKevrekidisPRE2014, copyright by APS 2014.
• Figure 2: Homoclinic orbit of the 2D map \ref{['equ:2Dmap']} for $c=1$, and $\omega=0.95.$. The dashed green line corresponds to the supratransmission threshold: $A_{thr}=1.255$.
• Figure 3: Spatiotemporal evolution for the discrete equation \ref{['equ1model']} with boundary driving condition \ref{['equ:driven']}. The parameters are $f=0$, $c=1$, $\omega=0.95.$ and $A=1.254< A_{thr}$
• Figure 4: Spatiotemporal evolution for the discrete equation \ref{['equ1model']} with boundary driving condition \ref{['equ:driven']}. The parameters are $f=0$, $c=1$, $\omega=0.95.$ and $A=1.256>A_{thr}$.
• Figure 5: Spatiotemporal evolution of the lattice submitted to periodic horizontal shaking: $f=0.2$; $c=1$; $\omega_{1}=0.95$.