Abstract
In this study, the parametric resonances of pinned intrinsic localized modes (ILMs) were investigated by computing the unstable regions in parameter space consisting of parametric excitation amplitude and frequency. In the unstable regions, the pinned ILMs were observed to lose stability and begin to fluctuate. A nonlinear Klein–Gordon, Fermi–Pasta–Ulam-like, and mixed lattices were investigated. The pinned ILMs, particularly in the mixed lattice, were destabilized by parametric resonances, which were determined by comparing the shapes of the unstable regions with those in the Mathieu differential equation. In addition, traveling ILMs could be generated by parametric excitation.
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