The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables. (English) Zbl 1005.70023

Manevitch, L. I.

Nonlinear Dyn. 25, No. 1-3, 95-109 (2001).

Summary: We present an asymptotic approach to the analysis of coupled nonlinear oscillators with asymmetric nonlinearity based on the complex representation of dynamic equations. The ideas of the approach are first developed for a system with two degrees of freedom. Special attention is paid to the study of localized normal modes in a chain of weakly coupled nonlinear oscillators. We also discuss certain features of the localization of excitations in the case of strong coupling between the oscillators.

MSC:

70K99

Nonlinear dynamics in mechanics

Keywords:

weak coupling; coupled nonlinear oscillators; asymmetric nonlinearity; complex representation; localized normal modes; strong coupling