Extraordinary electromagnetic localized structures in plasmas: Modulational instability, envelope solitons, and rogue waves

•We have considered the nonlinear propagation of extraordinary waves in a transversely magnetized plasmas.•The existence condition for nonlinear structures e.g. envelope solitons and rogue waves are examined.•Modulational instability of extraordinary waves has been addressed.

We have considered the nonlinear propagation of an extraordinary electromagnetic wave in a transversely magnetized plasma. It is found that, in a weakly relativistic regime, evolution of the amplitude of an extraordinary wave packet is governed by a nonlinear Schrödinger (NLS) equation. The modulational instability of an extraordinary plane wave is investigated. The analytical solutions of the NLS equation in the forms of envelope solitons and rogue waves are reviewed and dependence of their structural properties on relevant parameters of the system is addressed.