Eckhaus Instability in the Lugiato-Lefever model

Nicolas Perinet, Nicolas Verschueren van Rees, Saliya Coulibaly

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)
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We study theoretically the primary and secondary instabilities undergone by the stationary periodic patterns in the Lugiato-Lefever equation in the focusing regime. Direct numerical simulations in a one-dimensional periodic domain show discrete changes of the periodicity of the patterns emerging from unstable homogeneous steady states. Through continuation methods of the steady states we reveal that the system exhibits a set of wave instability branches. The organisation of these branches suggests the existence of an Eckhaus scenario, which is characterized in detail by means of the derivation of their amplitude equation in the weakly non regime. The continuation in the highly nonlinear regime shows that all the branches become unstable through a Hopf bifurcation.
Original languageEnglish
Article number243
Number of pages10
JournalEuropean Physical Journal D
Early online date26 Sept 2017
Publication statusPublished - Sept 2017


  • Dynamics of nonlinear optical systems
  • optical instabilities
  • optical chaos and complexity
  • optical spatio-temporal dynamics


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