Long-wave and short-wave asymptotics in nonlinear dispersive systems

In this paper we study the interplay between short- and long-space scales i n the context of conservative dispersive systems. We consider model systems in (1+1) dimensions that admit both long- and short-wavelength solutions i n the linear regime. A nonlinear analysis of these systems is constructed, making use of multiscale expansions. We show that the equations governing t he lowest order involve only short-wave-properties and that the long-wave e ffects to leading order are determined by a secularity elimination procedur e. [S1063-651X(99)02708-7].