Kullback-Leibler quantum divergence as an indicator of quantum chaos

► A nonlinear Kerr-like oscillator pumped by ultra-short coherent pulses is discussed. ► The Kullback-Leibler quantum divergence is analysed as an detector of quantum chaos. ► Linear and nonlinear quantum divergences and their power spectra are applied. ► The divergences are more adequate chaosʼs indicators than those based on fidelity. ► Defined nonlinear parameters are useful for dealing with short time series.