One-dimensional modulation instability of wave packets in media with resonant dispersion

Modulation instability of small-amplitude quasimonochromatic wave packets in media containing compact oscillators is analysed in the one-dimensional case. Conservative media with quadratic nonlinearity and linear nondamped oscillators are considered. Frequency range of unstable wave-packet propagation is found. It is shown that instability results from resonant long-wave-short-wave interaction.