1. Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping
- Author
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Hubert Branger, Debbie Eeltink, Maura Brunetti, Jérôme Kasparian, Christopher Luneau, Andrea Armaroli, University of Geneva, Université de Genève = University of Geneva (UNIGE), Institut Pythéas (OSU PYTHEAS), Institut de Recherche pour le Développement (IRD)-Aix Marseille Université (AMU)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Université de Genève (UNIGE), University of Geneva [Switzerland], and Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut de Recherche pour le Développement (IRD) more...
- Subjects
Truncation ,Plane wave ,FOS: Physical sciences ,Aerospace Engineering ,NLS ,Ocean Engineering ,Pattern Formation and Solitons (nlin.PS) ,ddc:500.2 ,Space (mathematics) ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,0103 physical sciences ,Phase-shift ,Symmetry breaking ,[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] ,Electrical and Electronic Engineering ,010306 general physics ,Nonlinear Schrödinger equation ,Envelope (waves) ,Physics ,Original Paper ,Forcing (recursion theory) ,Applied Mathematics ,Mechanical Engineering ,Fluid Dynamics (physics.flu-dyn) ,Separatrix crossing ,Physics - Fluid Dynamics ,Fundamental frequency ,Nonlinear Sciences - Chaotic Dynamics ,Nonlinear Sciences - Pattern Formation and Solitons ,Control and Systems Engineering ,Gravity surface waves ,Quantum electrodynamics ,symbols ,Chaotic Dynamics (nlin.CD) - Abstract
We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schr\"odinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation of the spectrum. In the latter, only the fundamental frequency and the upper and lower sidebands are retained. Plane wave solutions to the NLSE exhibit modulation instability (MI) within a frequency band determined by a linear stability analysis. For modulation frequencies inside the MI-band, we experimentally demonstrate that forcing and damping cause a separatrix crossing during the evolution. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general. When the system is damped by the viscosity of the water, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi-Pasta-Ulam-Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside the separatrix. Furthermore, for modulation frequencies outside the conventional MI-band, we experimentally demonstrate that contrary to the linear prediction, we do observe a growth and decay cycle of the plane-wave modulation. Finally, we give a theoretical demonstration that forcing the NLSE system can induce symmetry breaking during the evolution., Comment: 12 pages, 9 figures more...
- Published
- 2020
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