Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation

Details Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation

2012-02-26

arxiv.org/abs/1202.5763v1

Physics

Optics

10 pages, 26 figures

Scientific paper

We measure evolution of spectra, spatial correlation functions and probability density functions (PDF) of waves appearance for one-dimensional generalized Nonlinear Schrodinger equation: (1) accounting for six- and eight-wave interactions terms and (2) accounting for six-wave interactions, dumping (linear dissipation and three-photon absorption) and pumping terms. All additional terms beyond the classical NLS equation are small. We observe strongly non-Gaussian PDFs with "fat tails" in the region of large amplitudes when higher waves appear more frequently. For generalized NLS equation with six-wave interactions, dumping and pumping terms we demonstrate absence of non-Gaussian addition to PDF for zeroth six-wave interactions coefficient and increase of non-Gaussian addition with six-wave interactions term.

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