The problem of nonlinear self-focusing of elliptic Gaussian laser beam
in collisionless magnetized plasma is studied using variation approach.
The dynamics of the combined effects of nonlinearity and spatial
diffraction is presented. With a and b as the beam width
parameters of the beam along x and y directions, respectively, the
phenomenon of cross-focusing is observed where focusing of a
results in defocusing of b and vice versa. Although no stationary
self-trapping is observed, oscillatory self-trapping occurs far below the
threshold. The regularized phase is always negative.
