Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium

Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of non-linearity and diffraction on wa ve propagation of optical beam in a homogeneous bulk Kerr-medium is present ed. Particular emphasis is put on the variation of beam width and longitudi nal phase delay with the distance of propagation. It is observed that no st ationary self-trapping is possible. The regularized phase is also seen to b e always negative.