  The conservation of spectral asymmetry is a fundamental feature of the ideal
four-wave mixing process as it exists in a medium combining quadratic chromatic
dispersion and third-order nonlinearity. We test in this paper the robustness
of this invariant in an experimental configuration where the excitation
conditions of an optical fiber are sequentially updated, mimicking infinite
propagation. This theoretical and experimental study reveals the high
sensitivity of the asymmetry to very slight deviations from the ideal case, and
we show that our idealized system behaves as an intermediate case between the
ideal case of non-cascaded fourwave mixing and propagation in a system governed
by the nonlinear Schr{\"o}dinger equation.
