WIAS Preprint No. 2934, (2022)

Unusual ways of four-wave mixing instability


  • Amiranashvili, Shalva
    ORCID: 0000-0002-8132-882X
  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347

2020 Mathematics Subject Classification

  • 78A40 78A60


  • Nonlinear fibers, modulation instability, four wave mixing instability, Lighthill criterion, negative frequencies




A pump carrier wave in a dispersive system may decay by giving birth to blue- and red-shifted satellite waves due to modulation or four-wave mixing instability. We analyse situations where the satellites are so different from the carrier wave, that the red-shifted satellite either changes its propagation direction (k < 0, ω > 0) or even gets a negative frequency (k, ω < 0). Both situations are beyond the envelope approach and require application of Maxwell equations.

Appeared in

  • Phys. Rev. A, 105 (2022), pp. 063519/1--063519/6, DOI 10.1103/PhysRevA.105.063519 with the new title ``Unusual scenarios in four-wave-mixing instability''.

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