Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence

Research output: Contribution to journalArticleScientificpeer-review


  • O. Kimmoun
  • H. C. Hsu
  • H. Branger
  • M. S. Li
  • Y. Y. Chen
  • C. Kharif
  • M. Onorato
  • E. J R Kelleher
  • B. Kibler
  • N. Akhmediev
  • A. Chabchoub

Research units

  • National Cheng Kung University
  • Imperial College London
  • Australian National University
  • Laboratoire Interdisciplinaire Carnot de Bourgogne
  • University of Tokyo
  • Aix-Marseille Université
  • Universita degli Studi di Torino


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.


Original languageEnglish
Article number28516
Number of pages9
JournalScientific Reports
Publication statusPublished - 20 Jul 2016
MoE publication typeA1 Journal article-refereed

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