ABSTRACT
When we try to understand the qualitative dynamics of spatially extended nonlinear systems through mathematical analysis, we require theoretical tools to reduce the governing dynamical laws to simpler forms. Thus it is natural to ask under what general conditions such model reduction can be achieved. A possible answer is that the reduction is possible when the system involves a few special degrees of freedom whose dynamics is distinctively slower, i.e. whose characteristic time scales are far longer than those of the remaining degrees of freedom: then those degrees of freedom with short time scales may either be eliminated adiabatically or cancelled as a result of time-averaging of their rapid changes. The existence of slow variables is thus crucial to the reduction. Here ‘slow’ implies that the stability is almost neutral, so that we may call such slow degrees of freedom neutral modes.
