We present a numerical method to deal with the propagation of a short and highly intense laser pulse in an underdense plasma, leading to relativistic self-focusing and wakefield effect. By assuming that the temperature is low enough and that there is no wave-breaking, we write hydrodynamic equations, coupled to Maxwell's equations. We treat them by a time splitting method, which stability is studied, and by a finite difference/volume method in space. A discrete version of Gauss' equation is preserved with time, so that no Poisson correction is needed. The code is consequently fully local and explicit. Results from two-dimensional simulations are presented.

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