Bispectral analysis of nonlinear mixing in a periodically driven Korteweg-de Vries system

TL;DR

This study uses bispectral analysis to investigate nonlinear wave mixing in a driven Korteweg-de Vries system, revealing how different drivers influence spectral responses and the dominance of three-wave interactions.

Contribution

It demonstrates that nonlinear drivers like cnoidal and traveling waves produce spectral responses closer to experiments and clarifies the role of three-wave mixing in nonlinear oscillations.

Findings

Nonlinear drivers yield spectral responses similar to experimental data.

Three-wave mixing predominantly governs nonlinear oscillations.

Driver frequency and form influence the spectral pattern from broad to sparse.

Abstract

The nonlinear response of a periodically driven Korteweg-de Vries model system is studied using a variety of nonlinear drivers and compared to previous results obtained for a purely time-dependent sinusoidal driver [Phys. Plasmas 27, 113701 (2020)]. It is found that a nonlinear driver in the form of a cnoidal square wave or a travelling wave driver produces a spectral response that is closer to experimental observations [Phys. Rev. Lett. 92, 085001 (2004)] than that predicted by the simple sinusoidal driver. Using a bispectral analysis, we also firmly establish that the nature of the nonlinear oscillations, due to the interaction between the periodic source and the inherent collective mode of the system, is predominantly governed by a three-wave mixing process. Furthermore, by studying the variation in the mixing pattern, from a broad to a sparse frequency spectrum, as a function of the driver frequency and its functional form, we propose a means of tailoring the nature of such patterns. Our results could find useful applications in the experimental interpretation and manipulation of nonlinear wave mixing patterns in weakly nonlinear and dispersive plasma systems or similar phenomena in neutral fluids.