title: Long-wave and short-wave asymptotics in nonlinear dispersive systems.
abstract: In this paper we study the interplay between short- and long-space scales in the context of conservative dispersive systems. We consider model systems in (1+1) dimensions that admit both long- and short-wavelength solutions in the linear regime. A nonlinear analysis of these systems is constructed, making use of multiscale expansions. We show that the equations governing the lowest order involve only short-wave properties and that the long-wave effects to leading order are determined by a secularity elimination procedure.
authors.affiliation: Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 São Paulo, Brazil.
authors.forename: R A
authors.initials: RA
authors.lastname: Kraenkel
authors.forename: M A
authors.initials: MA
authors.lastname: Manna
authors.forename: V
authors.initials: V
authors.lastname: Merle