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

Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. New localized structures, in the form of exact \Changes{numerical} nonlinear solutions of the one-dimensional Maxwell-fluid model for a cold plasma with fixed ions are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breather-like behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finite-differences scheme allows to compute a branch of solutions within the frequency range $Ω_{min}<Ω<ω_{pe}$, where $ω_{pe}$ and $Ω_{min}$ are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatio-temporal structure of the waves and their main properties as a function of $Ω$ are presented. Direct numerical simulations of the Maxwell-fluid model show that these solitary waves propagate without change for a long time.

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