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 by Mir et al. [Phys. Plasmas 27, 113701 (2020)]. It is found that a nonlinear driver in the form of a cnoidal-square wave or a traveling wave driver produces a spectral response that is closer to experimental observations of Nosenko et al. [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 mixing patterns, 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.