title: Solitons in strongly driven discrete nonlinear Schrödinger-type models.
abstract: Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear Schrödinger (DNLS) equations with damping and strong rapid drive are investigated. The averaged equations have the forms of the parametric AL and DNLS equations. An additional type of parametric bright discrete soliton and cnoidal waves are found and the stability properties are analyzed. The analytical predictions of the perturbed inverse scattering transform are confirmed by the numerical simulations of the AL and DNLS equations with rapidly varying drive and damping.
authors.affiliation: Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 5, France. garnier@math.jussieu.fr
authors.forename: Josselin
authors.initials: J
authors.lastname: Garnier
authors.forename: Fatkhulla Kh
authors.initials: FKh
authors.lastname: Abdullaev
authors.forename: Mario
authors.initials: M
authors.lastname: Salerno