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By using perturbation theory we derive an expression for the electrical fieldof a Gaussian laser pulse propagating in a gas medium. This expression is usedas a trial solution in a variational method to get quasianalytical solutionsfor the width, intensity and self-focusing distance of ultrashort pulse. Theapproximation gives an improved agreement with results of numerical simulationsfor a broad range of values of the input power of the pulse than previousanalytical results available in the literature.Comment: 19 pages, 8 figure

Variational analysis of self-focusing of intense ultrashort pulses in gases