Existence of discrete rogue waves in a purely driven pendulum chain

Determine whether discrete rogue waves can be generated in the torsionally coupled pendulum chain governed by the dimensionless equation \eqref{equ1model} when the lattice is only boundary-driven at one edge with no parametric horizontal shaking (forcing coefficient f = 0), i.e., in the "just driven, not shaken" case.

Background

The paper studies a chain of pendula connected by torsional springs and subject to different types of excitations: boundary driving, parametric shaking, and both simultaneously. It demonstrates the standard supratransmission phenomenon under edge driving, trapping behavior under shaking, and the emergence of discrete rogue waves when the system is simultaneously driven and shaken.

The authors explicitly remark that while they have observed discrete rogue waves under simultaneous driving and shaking, they have not yet observed such events in the purely driven (not shaken) configuration. They highlight uncertainty about whether rogue waves can arise in that case, thus posing an explicit open question about their existence in a simpler driving-only setup.