Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence.
Olivier Kimmoun,Hung-Chu Hsu,Hubert Branger,M. S. Li,You Yi Chen,C. Kharif,Miguel Onorato,Edmund J. R. Kelleher,Bertrand Kibler,Nail Akhmediev,Amin Chabchoub +10 more
TLDR
Evidence is reported of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order, and it is shown that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics.Abstract:
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. One prominent form of instability in a distributed system is its response to a harmonic modulation. Such instability has special names in various branches of physics and is generally known as modulation instability (MI). The MI leads to a growth-decay cycle of unstable waves and is therefore related to Fermi-Pasta-Ulam (FPU) recurrence since breather solutions of the nonlinear Schrodinger equation (NLSE) are known to accurately describe growth and decay of modulationally unstable waves in conservative systems. Here, we report theoretical, numerical and experimental evidence of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order. In showing that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics, our results may impact the interpretation of a wide range of new physics scenarios.read more
Citations
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Journal ArticleDOI
Fibre multi-wave mixing combs reveal the broken symmetry of Fermi-Pasta-Ulam recurrence
Arnaud Mussot,Corentin Naveau,Matteo Conforti,Alexandre Kudlinski,François Copie,Pascal Szriftgiser,Stefano Trillo +6 more
TL;DR: In this article, the evolution in amplitude and phase of frequency modes is reconstructed via post-processing of the fiber backscattered light. But the proposed technique is an important tool to characterize other mixing processes and new regimes of rogue wave formation and wave turbulence in fibre optics.
Journal ArticleDOI
Observation of Fermi-Pasta-Ulam-Tsingou Recurrence and Its Exact Dynamics
Davide Pierangeli,Davide Pierangeli,M. Flammini,Long Zhang,Giulia Marcucci,Aharon J. Agranat,Petr Georgievich Grinevich,Petr Georgievich Grinevich,P. M. Santini,P. M. Santini,Claudio Conti,Eugenio DelRe +11 more
TL;DR: In this paper, the authors reveal the origin of the enigma of the recurrence of initial conditions in nonlinear dynamics and demonstrate the ability to reconstruct the initial condition of an unstable system.
Journal ArticleDOI
Rogue waves on the double-periodic background in the focusing nonlinear Schrödinger equation
TL;DR: The double-periodic solutions of the focusing nonlinear Schrödinger equation are constructed by using an algebraic method with two eigenvalues and the Lax spectrum is characterized and rogue waves arising on the background of such solutions are analyzed.
Journal ArticleDOI
Nonlinear Evolution of the Locally Induced Modulational Instability in Fiber Optics
TL;DR: In this paper, an optical fiber experiment was conducted to study the nonlinear stage of modulational instability of a plane wave in the presence of a localized perturbation, and it was shown that the initial perturbations evolved into an expanding nonlinear oscillatory structure exhibiting some universal characteristics that agree with theoretical predictions based on integrability properties of the focusing nonlinear Schrodinger equation.
Journal ArticleDOI
The Physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: rogue waves, modulation instability and self-focusing phenomena
TL;DR: In this paper, different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schrodinger equation (1DNLSE) in the focusing regime are reviewed.
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