Self-action of intense electromagnetic radiation in an electron-positron vacuum

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Abstract
An analysis is done of the effects of self-action of intense coherent electromagnetic radiation in an electron-positron vacuum that is in homogeneous electric and magnetic fields. A modified version of the Heisenberg-Euler theory, in which the Lagrangian incorporates terms with field derivatives, is used to take into account vacuum dispersion. The nonphysical branch of the solutions of the dispersion equation is excluded by a transition to a quasioptical equation for the slowly varying field envelope, an equation that describes the propagation of radiation with allowance for diffraction, spatial-temporal dispersion, and vacuum nonlinearity. The existence of dark solitons (with an intensity gap) in the vacuum is shown to be present. Finally, self-focusing of radiation in a vacuum is demonstrated and the critical self-focusing power is determined.