The influence of electron trapping on the propagation of an electrosound wave is investigated. It is shown, that on the stage of modulational instability the trapped particles prevent the spatial localization of the HF field. Under certain conditions the trapped particles destroy the stationary soliton. For nonstationary envelope waves the nonlinearity, connected with trapped particles, leads to a Korteveg-de Vries equation.

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By using a relativistic fluid model, a nonlinear theory for the propagation of an intense laser pulse in an inhomogeneous cold plasma is developed. Assuming that the radiation spot size is larger than the plasma wavelength, we derive an envelope equation for the momentum of the electron fluid, taking into account relativistic electron mass variation and finite amplitude electron density perturbations that are driven by the relativistic ponderomotive force of light. Localized solutions of the envelope equation are discussed from an energy integral containing an effective potential. Numerical results for envelope solitons are obtained in a quasistationary approximation. The dependency of these localized solutions on the amplitude and the group velocity of the laser pulse is discussed. Also derived is an equation that governs the dynamics of the pulse center.