Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation
Pattern Formation and Solitons
2016-07-06 v1 Exactly Solvable and Integrable Systems
Optics
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.
Keywords
Cite
@article{arxiv.1606.01658,
title = {Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation},
author = {M. Conforti and A. Mussot and A. Kudlinski and S. Rota-Nodari and G. Dujardin and S. De Bievre and A. Armaroli and S. Trillo},
journal= {arXiv preprint arXiv:1606.01658},
year = {2016}
}