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Summary form only given. The problem of nonlinear self-focusing of elliptic Gaussian laser beams is reformulated in terms of a variational principle. The dynamics of combined effects of nonlinearity and spatial diffraction on self-phase modulation of the laser beam propagating in dispersionless collisionless plasma is presented. It is further shown that the self-trapping increases with the decrease in ellipticity. It is also observed that at fixed wavelength and intensity, the ellipticity shows marked difference in propagation characteristics and self-phase modulation.