Integrable turbulence and formation of rogue waves

2014/09/30 by D. S. Agafontsev, V. E. Zakharov · 4 citations
Physics and Astronomy · #nlin.SI #physics.flu-dyn

paper · pdf · doi:10.1088/0951-7715/28/8/2791

published as Nonlinearity 28 (2015) 2791-2821 · 42 pages, 24 figures

arxiv created 2015/09/12 · arxiv updated 2015/09/15

Abstract

In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable turbulence" [V.E. Zakharov, Turbulence in integrable systems, Stud. in Appl. Math. 122, no. 3, 219-234, (2009)]. We study the time evolution of it's major characteristics averaged across realizations of initial data - the condensate solution seeded by small random noise with fixed statistical properties. The measured quantities are: (1) wave-action spectrum and spatial correlation function, (2) the probability density function (PDF) of wave amplitudes and their momenta, and (3) kinetic and potential energies.

Cited by

• Rogue waves from noise-induced modulational instability of a plane wave
• Soliton gas resolution and statistics of random wave fields in semiclassical integrable turbulence
• Rogue wave statistics and integrable turbulence in the Gerdjikov-Ivanov equation
• Bidirectional shallow-water wave turbulence

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