Multiple-Scale Approach to Nonlinear Phase Dynamics

Abstract

A fundamental equation of the phase dynamics is derived for a class of periodic structures by a systematic application of the multiple-scale expansion method, in which the instantaneous rate of change of the phase is shown to be determined only by the local values of spatial derivatives of the phase itself. The analys is shows that the phase equation is inapplicable to conservative systems. The expansion method is also applied to a class of forced periodic structures, and the same type of equation is derived although the dependent variable then does not correspond to the phase of the periodic structure.