Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons.

Dissipative media admit the existence of two types of stationary self-organized beams: continuously self-focused and continuously self- defocused. Each beam is stable inside of a certain region of its existence. Beyond these two regions, beams loose their stability, and new dynamical behaviors appear. We present several types of instabilities related to each beam configuration and give examples of beam dynamics in the areas adjacent to the two regions. We observed that, in one case beams loose the radial symmetry while in the other one the radial symmetry is conserved during complicated beam transformations.