Modulational instability in transversely connected nonlinear pendulum pairs

In this work, we investigate the modulational instability (MI) phenomenon in a chain of coupled pendulum pairs, where each pendulum is connected to the nearest neighbors in the longitudinal and transverse directions. Based on the obtained equation describing the dynamics of the model, we derive the coupled discrete nonlinear Schrodinger equation using the multiple scale method. We use the obtained coupled discrete nonlinear Schrodinger equation to study the possibility of modulational instability. The linear stability analysis leads us to obtain the growth rate of the MI. It reveals that the instability growth rate and MI band are dramatically affected by the transverse coupling parameter. Finally, we use the MI analysis to study the dynamics of the generated unstable plane wave solutions numerically. This confirms that the existence of MI in the lattice leads to the breakup of wave into periodic localized pulses which have the shape of soliton-like objects.