Topological transformations of three-dimensional dissipative solitons in the framework of the generalized Ginzburg–Landau equation

We classify and analyze transformations of three-dimensional dissipative tangle-solitons, i.e., solitons with closed and nonclosed vortex lines, under smooth variations of the system parameters. An example of such a system is a laser medium with fast saturable absorption. We find several scenarios of both reversible and irreversible transformations and discuss the role of the dissipative property of the system (openness) in specific features of these phenomena.