Abstract
The nonlinear propagation of two circularly polarized strong laser pulses in a magnetized plasma is considered. In a weakly relativistic regime, it is shown that the evolution of amplitudes of the laser pulses is governed by two coupled cubic nonlinear Schrödinger (NLS) equations. The modulational instability of coupled plane wave solutions is investigated based on coupled NLS equations. The dependence of the growth rate on relevant parameters of the system is addressed. The possibility of formation of various kinds of coupled solitary wave solutions in magnetized and unmagnetized cases is considered, and the variation of the profile of these solutions with different parameters is explored.
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