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

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.

arXiv comment13 pages, 7 figures, 3 tables

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• Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma
• Experimental evidence of a hydrodynamic soliton gas
• Experimental observation of precursor solitons in a flowing complex plasma
• Dynamics of Bose-Einstein condensates in cigar-shaped traps
• Ion-acoustic cnoidal waves in a quantum plasma
• Experimental observation of pinned solitons in a flowing dusty plasma
• Precursor magneto-sonic solitons in a plasma from a moving charged object
• High frequency sheath modulation and higher harmonic generation in a low pressure very high frequency capacitively coupled plasma excited by sawtooth waveform
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Cited by in corpus (4)

• Synchronization of Dust Acoustic Waves in a forced Korteweg-de Vries-Burgers model
• Modeling of Experimentally Observed Two-Dimensional Precursor Solitons in a Dusty Plasma by the forced Kadomtsev-Petviashvili Equation
• Nonlinear dispersion relation of dust acoustic waves using the Korteweg-de Vries model
• Nonlinear Mixing of Waves in a Yukawa One Component Plasma