General properties of transient self-interactions in media with a relaxing cubic nonlinearity

It is shown that self-interactions of laser beams are invariant under several transformations such as similarity, reflection, lens, and other operations. Transformations are derived for conversion of a diffracted beam into a converging or diverging form with a different initial cross section but the same power. This makes it possible to compare the results of experiments carried out using different beams. Invariant transformations are retained in the aberration-free description of the self-focusing of Gaussian beams.