Intermittency in generalized NLS equation with focusing six-wave interactions

TL;DR

This paper numerically investigates the statistical behavior of waves in a generalized NLS equation with six-wave interactions, revealing universal non-Rayleigh statistics and strong intermittency influenced by six-wave coupling.

Contribution

It demonstrates the universal statistical behavior and intermittency effects in a generalized NLS system with six-wave interactions, highlighting the role of these interactions in wave amplitude distributions.

Findings

Probability density function exhibits fat tails for large waves.

Intermittency increases with six-wave coupling coefficient.

Non-Rayleigh statistics vanish without six-wave interactions.

Abstract

We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrodinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic "fat tail" decaying with amplitude $|\Psi|$ close to $\propto\exp(-\gamma|\Psi|)$, where $\gamma>0$ is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.