Abstract
The evolution of an optical beam in a graded-index single-mode nonlinear optical fibre is treated by means of a variational principle. Approximate analytic solutions are obtained for the propagation characteristics of a cw Gaussian beam profile in the nonlinear optical fibre. We demonstrate that spot width variations depend only on a single parameter which encapsulates the dynamical interplay of diffraction, waveguiding, and nonlinear effects. Based on this parameter we can distinguish diffraction and self-focusing dominated regimes, and in a straight forward manner obtain the self-trapping and self-focusing conditions.