Direct verification of the kinetic description of wave turbulence for finite-size systems dominated by interactions among groups of 6 waves

TL;DR

This paper verifies when the wave kinetic equation accurately predicts the ensemble-averaged dynamics of finite-size systems with six-wave interactions, using the nonlinear Schrödinger equation as a model.

Contribution

It provides theoretical predictions and direct verification for the regimes where wave kinetic equations are valid for systems with six-wave interactions.

Findings

Wave kinetic equation accurately describes ensemble dynamics in specific regimes.

Theoretical predictions match numerical solutions of the dynamical equations.

Conditions where wave kinetic theory fails are also discussed.

Abstract

The present work considers systems whose dynamics are governed by the nonlinear interactions among groups of 6 nonlinear waves, such as those described by the unforced quintic nonlinear Schr\"odinger equation. Specific parameter regimes in which ensemble-averaged dynamics of such systems with finite size are accurately described by a wave kinetic equation, as used in wave turbulence theory, are theoretically predicted. In addition, the underlying reasons that the wave kinetic equation may be a poor predictor of wave dynamics outside these regimes are also discussed. These theoretical predictions are directly verified by comparing ensemble averages of solutions to the dynamical equation with corresponding solutions of the wave kinetic equation.