title: Heteroclinic Structure of Parametric Resonance in the Nonlinear Schrödinger Equation.
abstract: We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearized Floquet analysis.
authors.affiliation: Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France.
authors.forename: M
authors.initials: M
authors.lastname: Conforti
authors.affiliation: Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France.
authors.forename: A
authors.initials: A
authors.lastname: Mussot
authors.affiliation: Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France.
authors.forename: A
authors.initials: A
authors.lastname: Kudlinski
authors.affiliation: IMB UMR 5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France.
authors.forename: S
authors.initials: S
authors.lastname: Rota Nodari
authors.affiliation: Univ. Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé; Equipe MEPHYSTO, INRIA, F-59000 Lille, France.
authors.forename: G
authors.initials: G
authors.lastname: Dujardin
authors.affiliation: Univ. Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé; Equipe MEPHYSTO, INRIA, F-59000 Lille, France.
authors.forename: S
authors.initials: S
authors.lastname: De Biévre
authors.affiliation: FOTON (CNRS-UMR 6082) Université de Rennes 1, ENSSAT, 6 rue de Kerampont, CS 80518, F-22305 Lannion Cedex, France.
authors.forename: A
authors.initials: A
authors.lastname: Armaroli
authors.affiliation: Dipartimento di Ingegneria, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy.
authors.forename: S
authors.initials: S
authors.lastname: Trillo