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We studied integrable turbulence using the nonlinear Schrödinger equation and optical fibers. Our findings reveal two stages of turbulence development, offering new insights into wave intensity statistics.

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Area of Science:

  • Nonlinear physics
  • Wave phenomena
  • Fluid dynamics

Background:

  • Integrable turbulence (IT) is a complex phenomenon observed in nonlinear systems.
  • The defocusing cubic one-dimensional nonlinear Schrödinger equation is a key model for studying IT.
  • Previous research has explored IT, but a detailed understanding of its developmental stages and statistical properties remains incomplete.

Purpose of the Study:

  • To theoretically and experimentally investigate integrable turbulence (IT) within the framework of the defocusing cubic one-dimensional nonlinear Schrödinger equation.
  • To elucidate the distinct stages of IT development and explain the statistical properties of wave intensity.
  • To introduce Riemann invariants as observable quantities for analyzing the initial stage of IT.

Main Methods:

  • Theoretical analysis using a dispersive-hydrodynamic approach.
  • Experimental realization using an optical fiber setup with dominant defocusing Kerr nonlinearity.
  • Analysis of wave intensity statistics and probability density functions.

Main Results:

  • Identified two distinct stages in the development of IT: an initial, prebreaking stage and a subsequent stage.
  • Described the initial stage of IT using a system of interacting random Riemann waves.
  • Explained the observed low-tailed statistics of wave intensity in IT.
  • Demonstrated that Riemann invariants of the asymptotic nonlinear geometric optics system exhibit stationary probability density functions.

Conclusions:

  • The development of integrable turbulence in the nonlinear Schrödinger equation can be clearly delineated into two stages.
  • Riemann invariants serve as valuable observable quantities, offering new insights into the statistical features of the initial IT development.
  • The study provides a comprehensive understanding of IT, bridging theoretical predictions with experimental observations.