Unbounded Solutions of Coupled Mode Equations

Abstract

A number of sufficient conditions for the existence of unbounded solutions of two and three coupled mode equations are obtained when some modes are linearly unstable and all initial amplitudes are arbitrarily small. The difficulty of obtaining sufficient conditions for boundedness of all solutions is discussed, and only two such conditions are obtained. In certain cases it is proved that the unbounded solutions are not more rapid than exponential, whereas they can be shown to be singular (``explosive'') in other cases.