Integrable turbulence developing from strongly nonlinear partially coherent waves

Abstract

We study numerically the integrable turbulence developing from strongly nonlinear partially coherent waves, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. We find that shortly after the beginning of motion the turbulence enters a state characterized by a very slow evolution of statistics (the quasi-stationary state - QSS), and we concentrate on the detailed examination of the basic statistical functions in this state depending on the shape and the width of the initial spectrum. In particular, we show that the probability density function (PDF) of wavefield intensity is nearly independent of the initial spectrum and is very well approximated by a certain Bessel function representing an integral of the product of two exponential distributions. The PDF corresponds to the value of the second-order moment of intensity equal to 4, indicating enhanced generation of rogue waves. All waves of large amplitude that we have studied are very well approximated - both in space and in time - by the rational breather solutions of either the first (the Peregrine breather), or the second orders.

arXiv comment18 pages, 9 figures

References in corpus (14)

• Freak Waves in Random Oceanic Sea States
• Rogue waves and analogies in optics and oceanography
• Direct observation of Rogue Waves in optical turbulence using Time Microscopy
• Optical Rogue Waves in integrable turbulence
• Integrable turbulence and formation of rogue waves
• Universal Peregrine soliton structure in nonlinear pulse compression in optical fiber
• Statistical properties of nonlinear stage of modulation instability in fiber optics
• Integrable turbulence generated from modulational instability of cnoidal waves
• Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability
• Spontaneous emergence of rogue waves in partially coherent waves: a quantitative experimental comparison between hydrodynamics and optics
• Origin of heavy tail statistics in equations of the Nonlinear Schrödinger type: an exact result
• Optical Random Riemann Waves in Integrable Turbulence
• Effect of local Peregrine soliton emergence on statistics of random waves in the 1-D focusing Nonlinear Schrödinger equation
• Early stage of integrable turbulence in 1D NLS equation: the semi-classical approach to statistics

Cited by in corpus (8)

• Soliton gas in integrable dispersive hydrodynamics
• Statistics of extreme events in integrable turbulence
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• Experimental study of integrable turbulence in shallow water
• Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
• Bound-state soliton gas as a limit of adiabatically growing integrable turbulence
• Compressible vortex structures and their role in the onset of hydrodynamic turbulence
• Asymmetric integrable turbulence and rogue wave statistics for the derivative nonlinear Schrödinger equation