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Rogue wave modes for a derivative nonlinear Schrödinger model.

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Rogue waves in derivative nonlinear Schrödinger equations can occur with negative cubic nonlinearity, linked to modulation instability. Their maximum amplitude is three times the background, matching Peregrine breather results.

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Area of Science:

  • Fluid dynamics
  • Nonlinear optics
  • Wave phenomena

Background:

  • Rogue waves are large, unexpected wave displacements.
  • They appear in nonlinear Schrödinger equations with specific nonlinearity and dispersion regimes.

Purpose of the Study:

  • To investigate rogue waves in a derivative nonlinear Schrödinger equation.
  • To explore their occurrence in negative cubic nonlinearity regimes.
  • To connect rogue wave formation with modulation instability.

Main Methods:

  • Calculated rogue waves as a long-wave limit of a breather.
  • Analyzed the role of self-steepening nonlinearity.
  • Investigated the threshold for modulation instability.
  • Performed numerical simulations.

Main Results:

  • Rogue waves can occur in negative cubic nonlinearity with sufficient self-steepening.
  • The critical self-steepening magnitude matches the modulation instability threshold.
  • Maximum rogue wave amplitude is three times the background amplitude.
  • Results correlate with experimental water wave data.

Conclusions:

  • Rogue waves in this model are strongly linked to modulation instability.
  • The findings provide a theoretical basis for rogue wave occurrence in diverse nonlinear systems.
  • The study bridges theoretical calculations with experimental observations.