Boundary-condition effects in anharmonic lattice dynamics: Existence criteria for intrinsic localized modes from extended-mode properties

Recent theoretical studies of periodic one-dimensional anharmonic lattices with standard periodic boundary conditions established fundamental connections between the existence of intrinsic localized modes (ILM's) and the stability of the extended lattice modes into which they evolve with decreasing amplitude. While the odd-order anharmonicity drops out of the equations of motion far the extended modes within these boundary conditions, it nevertheless produces an amplitude-dependent period-averaged ''dynamical stress'' across the supercell boundaries. Here, we allow the supercell length to adjust so as to eliminate this stress and find that the frequency vs amplitude curves for the anharmonic extended modes are markedly changed for a variety of realistic nearest-neighbor interactions, whereas highly localized ILM's are little affected. Nevertheless, in all cases ILM existence remains intimately connected to an instability of the associated extended mode. Furthermore, the use of zero-stress periodic boundary conditions now allows one to predict the spatial extent of an ILM from extended-mode stability properties in lattices with odd-order anharmonicity. Most importantly, for the zero-stress periodic boundary conditions we obtain an additional ILM existence criterion, based on simple dynamical properties of the unperturbed related extended mode. Since well-localized ILMs are independent of the specific choice of boundary conditions, our results yield promising tools for ILM predictions in real systems.