Reversible and Irreversible Transformations of 3D-Tangle Laser Solitons

3D-topological solitons in laser media with fast saturable absorption are tangles, i.e. they have a number of unclosed and closed vortex lines where the field vanishes and electromagnetic energy twists [1,2]. Different types of these tangle laser solitons are stable within different, but overlapping domains of parameters. In [3] predicted is irreversible hysteresis of the solitons when such a control parameter as the small-signal gain g
₀
coefficient slowly increases crossing the boundary of the stability domain and then slowly decreases restoring its initial value. Here we study in more detail transformations of internal structure characterized by arrays of vortex lines of tangle laser solitons, induced, first, by variations of g
₀
and, second, by collisions of two solitons.