Modulated light pulses in which the modulation envelope propagates as an isolated solitary plasma wave are an interesting class of exact one dimensional nonlinear solutions of the relativistic cold plasma model. They have been investigated in great detail in recent years due to their potential applications in various intense laser plasma interaction scenarios including plasma based particle and photon acceleration schemes, fast ignition method of laser fusion and radiation dynamics around a pulsar. We review some of the interesting properties of these solitons and discuss a few fundamental issues related to their existence, spectral properties and the influence of ion dynamics and finite temperature effects. We also present a new class of solitary wave solutions that exhibit an oscillatory structure in the amplitude of the electrostatic potential.

A class of exact one-dimensional solutions of coupled nonlinear equations describing the propagation of a weakly relativistic circularly polarized electromagnetic pulse in a warm, collisionless and unbounded plasma is presented. The solutions investigated are in the form of a slowly moving dark or bright envelope soliton with a propagation velocity comparable to the thermal speed of the particles. For such a slowly propagating entity, the modulational envelope is strongly modified by the effects arising due to ion inertia as well as by the thermal effects of both ions and electrons. Different regions of existence of dark and bright solitons have been identified. The analysis carried out here is restricted to nearly quasi-neutral dynamics where the second derivative term in the Poisson equation plays a subsidiary role. Under this approximation, the eigenvalue problem has continuum solutions and one can establish the nonlinear relationship between the group velocity of the soliton and the amplitude and frequency of the light pulse.