title: Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence.
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 Schrödinger 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.
authors.affiliation: Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France.
authors.forename: O
authors.initials: O
authors.lastname: Kimmoun
authors.affiliation: Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan.
authors.forename: H C
authors.initials: HC
authors.lastname: Hsu
authors.affiliation: Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France.
authors.forename: H
authors.initials: H
authors.lastname: Branger
authors.affiliation: Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan.
authors.forename: M S
authors.initials: MS
authors.lastname: Li
authors.affiliation: Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan.
authors.forename: Y Y
authors.initials: YY
authors.lastname: Chen
authors.affiliation: Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France.
authors.forename: C
authors.initials: C
authors.lastname: Kharif
authors.affiliation: Dipartimento di Fisica Generale, Universita degli Studi di Torino, Torino, Italy.
authors.forename: M
authors.initials: M
authors.lastname: Onorato
authors.affiliation: Femtosecond Optics Group, Department of Physics, Imperial College London, London, UK.
authors.forename: E J R
authors.initials: EJ
authors.lastname: Kelleher
authors.affiliation: Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS UBFC, Dijon, France.
authors.forename: B
authors.initials: B
authors.lastname: Kibler
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University, Canberra ACT 020, Australia.
authors.forename: N
authors.initials: N
authors.lastname: Akhmediev
authors.affiliation: Department of Ocean Technology Policy and Environment, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan.|Department of Mechanical Engineering, Aalto University, 02150 Espoo, Finland.
authors.forename: A
authors.initials: A
authors.lastname: Chabchoub