Dynamics of irregular wave fields in the Schamel equation framework

TL;DR

This paper investigates how narrowband wave fields evolve within the non-integrable Schamel equation framework, using Monte Carlo simulations to analyze statistical properties influenced by nonlinearity and dispersion.

Contribution

It introduces a Monte Carlo approach to study the statistical dynamics of wave fields governed by the Schamel equation, highlighting the effects of nonlinearity and dispersion.

Findings

Spectral evolution varies with Ursell number

Moments and distribution functions are affected by nonlinearity

Simulation results reveal the impact of dispersion on wave dynamics

Abstract

The present article is devoted to the study of the dynamics of narrowband wave fields within the non-integrable Schamel equation, which plays an important role in plasma physics, wave dynamics in metamaterials, and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent realizations of the wave fields, allowing for an investigation of the evolution of the following statistical characteristics: spectra, moments, and distribution functions. The simulations are conducted for different values of the Ursell number (the ratio of nonlinearity to dispersion) to study the impact of nonlinearity and dispersion on the processes under consideration.