Розвиток інтегрованої турбулентності

Translated title of the contribution: Growing of integrable turbulence

D. S. Agafontsev, V. E. Zakharov

Research output: Contribution to journalArticlepeer-review


We study numerically the integrable turbulence in the framework of the focusing one-dimensional nonlinear Schrödinger equation using a new method - the “growing of turbulence”. We add to the equation a weak controlled pumping term and start adiabatic evolution of turbulence from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and realize that the “grown up” turbulence is statistically stationary. We measure its Fourier spectrum, the probability density function (PDF) of intensity and the autocorrelation of intensity. Additionally, we show that, being adiabatic, our method produces stationary states of the integrable turbulence for the intermediate moments of pumping as well. Presently, we consider only the turbulence of relatively small level of nonlinearity; however, even this “moderate” turbulence is characterized by enhanced generation of rogue waves.

Translated title of the contributionGrowing of integrable turbulence
Original languageUkranian
Pages (from-to)934-939
Number of pages6
JournalFizika Nizkikh Temperatur
Issue number8
Publication statusPublished - Aug 2020


  • Integrable turbulence
  • Nonlinear Schrödinger equation
  • Pumping


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