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arXiv · 1606.01658

Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation

M. Conforti·A. Mussot·A. Kudlinski·S. Rota-Nodari·G. Dujardin·S. De Bievre·A. Armaroli·S. Trillo
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Abstract

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger 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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M. Conforti, A. Mussot, A. Kudlinski, S. Rota-Nodari, G. Dujardin, S. De Bievre, A. Armaroli, S. Trillo. 2016-06-06. Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation. https://doi.org/10.1103/physrevlett.117.013901

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