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Linearly polarized solitary waves, arising from the interaction of an intenselaser pulse with a plasma, are investigated. New localized structures, in theform of exact \Changes{numerical} nonlinear solutions of the one-dimensionalMaxwell-fluid model for a cold plasma with fixed ions are presented. Unlikestationary circularly polarized solitary waves, the linear polarization givesrise to a breather-like behavior and a periodic exchange of electromagneticenergy and electron kinetic energy at twice the frequency of the wave. Anumerical method based on a finite-differences scheme allows to compute abranch of solutions within the frequency range$\Omega_{min}<\Omega<\omega_{pe}$, where $\omega_{pe}$ and $\Omega_{min}$ arethe electron plasma frequency and the frequency value for which the plasmadensity vanishes locally, respectively. A detailed description of thespatio-temporal structure of the waves and their main properties as a functionof $\Omega$ are presented. Direct numerical simulations of the Maxwell-fluidmodel show that these solitary waves propagate without change for a long time.

Relativistic breather-like solitary waves with linear polarization in cold plasmas