Interactions between impurities and nonlinear waves in a driven nonlinear pendulum chain

The influence of impurities on envelope waves in a driven nonlinear pendulum chain is investigated under a continuum-limit approximation. The impurities studied here are a single defect in pendulum length, that is, one of the pendulums has a slight longer or shorter length than the other pendulums in the chain. Numerical results show that impurities exert a strong influence on localized envelop waves including breathers and phase-mismatched (nontopological) kinks, and also on nonlocalized envelop waves including periodic waves and spatiotemporal chaos. We find that a short defective pendulum at higher driving frequency exerts a similar influence on nonlinear waves as a long defective pendulum does at low driving frequency [N. V. Alexeeva et al., Phys. Rev. Lett. 84, 3053 (2000)]. They possess a clear symmetry and equality.