Heteroclinic structure of parametric ...
Document type :
Compte-rendu et recension critique d'ouvrage
PMID :
Title :
Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation
Author(s) :
Conforti, Matteo [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Mussot, Arnaud [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Kudlinski, Alexandre [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Rota Nodari, Simona [Auteur]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Dujardin, Guillaume [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
de Biévre, Stephan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Armaroli, Andrea [Auteur]
Fonctions Optiques pour les Technologies de l'informatiON [FOTON]
Trillo, Stefano [Auteur]
Engineering Department [Ferrara]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Mussot, Arnaud [Auteur]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Kudlinski, Alexandre [Auteur]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Rota Nodari, Simona [Auteur]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Dujardin, Guillaume [Auteur]

Quantitative methods for stochastic models in physics [MEPHYSTO]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
de Biévre, Stephan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Armaroli, Andrea [Auteur]
Fonctions Optiques pour les Technologies de l'informatiON [FOTON]
Trillo, Stefano [Auteur]
Engineering Department [Ferrara]
Journal title :
PHYSICAL REVIEW LETTERS
Publisher :
American Physical Society
Publication date :
2016-06-27
ISSN :
0031-9007
HAL domain(s) :
Physique [physics]/Physique [physics]/Optique [physics.optics]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [en]
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, ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
ANR Project :
Centre Européen pour les Mathématiques, la Physique et leurs Interactions
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Fibres optiques topographiques : nouvelles perspectives en optique non-linéaire guidée
Amplificateur paramétrique fibré d'impulsions femtosecondes à haute énergie
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