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Area of Science:

  • Nonlinear physics
  • Wave phenomena
  • Statistical mechanics

Background:

  • Partially coherent waves (PCW) are superpositions of uncorrelated linear waves.
  • Long-time evolution of PCW leads to rogue waves and non-Gaussian statistics.
  • Rogue wave frequency increases with narrower initial spectra.

Purpose of the Study:

  • Investigate integrable turbulence from very narrow initial spectra in the focusing one-dimensional nonlinear Schrödinger equation.
  • Analyze the emergence and statistics of rogue waves in this limiting case.
  • Characterize the quasistationary state (QSS) and its properties.

Main Methods:

  • Numerical simulations of the focusing one-dimensional nonlinear Schrödinger equation.
  • Analysis of probability density functions (PDF) of intensity.
  • Comparison of observed rogue wave amplitudes with rational breather solutions.

Main Results:

  • Turbulence enters a long-lived quasistationary state (QSS) from very narrow initial spectra.
  • The PDF of intensity in the QSS is Bessel function-approximated and independent of the initial spectrum.
  • Rogue waves with amplitudes ten times the average are observed, matching rational breather solutions.

Conclusions:

  • The QSS exhibits heavy-tailed, non-Gaussian statistics, significantly increasing rogue wave probability.
  • The findings highlight the fundamental limiting case of PCW evolution and rogue wave formation.
  • Rational breather solutions accurately describe the largest rogue waves observed.