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 linearised Floquet analysis.
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Physical Review Letters, American Physical Society, 2016, 117 (1), 〈10.1103/PhysRevLett.117.013901〉
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Soumis le : lundi 20 juin 2016 - 09:49:09
Dernière modification le : vendredi 13 octobre 2017 - 13:52:04

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M. Conforti, A. Mussot, A. Kudlinski, S. Rota Nodari, G. Dujardin, et al.. Heteroclinic Structure of Parametric Resonance in the Nonlinear Schrödinger Equation. Physical Review Letters, American Physical Society, 2016, 117 (1), 〈10.1103/PhysRevLett.117.013901〉. 〈hal-01333882〉

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