Abstract
The equation governing the propagation of spiral beams in a non-linear medium is analysed. It is shown that, taking into account the saturation effect, spiral beams have a tube-like structure with a periodicity along the axis of a non-linear autoguide. A critical power is found which it is necessary to exceed in order to give rise to the indicated autoguided regime of the beam propagation. Furthermore, in this work a strict self-similar solution is obtained of a non-linear Schrodinger-type equation that describes the collapse of spiral beams, and a new class of self-similar solutions is found for the case of spherical symmetry.
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