The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables

We present an asymptotic approach to the analysis of coupled nonlinearoscillators with asymmetric nonlinearity based on the complexrepresentation of the dynamic equations. The ideas of the approach arefirst developed for the case of the system with two degrees of freedom.Special attention is paid to the study of localized normal modes in achain of weakly coupled nonlinear oscillators. We discuss also certainpeculiarities of the localization of excitations in the case of strongcoupling between the oscillators.