The modulation of weakly non-linear ion acoustic plasma waves near the marginal state of instability

Abstract

The modulation of a one-dimensional weakly non-linear quasimonochromatic ion acoustic plasma wave (the carrier) is considered. It is well known that the carrier is modulationally unstable for wavenumbers k larger than a critical wavenumber kc, and that when k is not near kc the modulations of the carrier are governed by a non-linear Schrodinger (NS) equation. The author shows that when k is near kc, and under certain assumptions, the modulations are governed by a modified form of the NS equation that involves higher-order non-linearities, and that the correct critical wavenumber for marginal modulational instability is slightly different from kc.