  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.
