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An analytical formulation is presented for envelope-type solutions of intense polarized electromagnetic waves propagating in cold unmagnetized plasmas. Induced charge separation is fully taken into account and nonlinearities due to mass variation of both electrons and ions are included. Localized solutions are found for the case of subluminous wave phase velocity. The spectrum of solutions (dependence of wave amplitude on the free parameters in the theory, phase velocity and frequency) is discussed and compared with previous analytical and numerical results.

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We consider electrostatic plasma modes along the open field lines of a rotating neutron star. Goldreich-Julian charge density in general relativity is analyzed for the neutron star with zero inclination. It is found that the charge density is maximum at the polar cap and it remains almost same in certain extended region of the pole. For a steady state Goldreich-Julian charge density we found the usual plasma oscillation along the field lines; plasma frequency resembles to the gravitational redshift close to the Schwarzschild radius. We study the nonlinear plasma mode along the field lines.From the system of equations under general relativity, a second order differential equation is derived. The equation contains a term which describes the growing plasma modes near Schwarzschild radius in a black hole environment. The term vanishes with the distance far away from the gravitating object. For initially zero potential and field on the surface of a neutron star, Goldreich-Julian charge density is found to create the plasma mode, which is enhanced and propagates almost without damping along the open field lines. We briefly outline our plan to extend the work for studying solitonpropagation along the open field lines of strongly gravitating objects.