Existence regions of longitudinal and transverse intrinsic localized modes in Fermi-Pasta-Ulam chain in two-dimensional plane

Abstract

Abstract:We model the Fermi-Pasta-Ulam lattice, in which masses move in a twodimensional plane, and identify different types of intrinsic localized modes (ILMs): longitudinal and transverse. The stability of the ILMs is evaluated by using characteristic multipliers. Longitudinal ILMs tend to be unstable because of the buckling effect of the chain. In contrast, transverse ILMs become stable if the chain is initially stretched. This difference between the longitudinal and the transverse ILMs is revealed by computing existence regions with respect to the angular frequency and the initial extension of the chain. The results show that the longitudinal ILMs tend to be stable in low-frequency and low-extension areas whereas the transverse ILMs become stable upon strongly stretching the chain.