Spatiotemporal solitons and vortices in graded-index multimode lossy fibers

We introduce a model of nonlinear multimode fibers with losses and gain. The model is based on the (3+1)-dimensional cubic-quantic complex Ginzburg-Landau equation (CGLE) with conservative and dissipative nonlinearities and a 2- dimensional transverse trapping potential. It applies to passively mode-locked lasers in the short-pulse operation regime. Systematic numerical analysis of the model reveals a variety of stable modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number n =1 , while vortices with n = 2 are unstable, splitting into persistently rotating bound states of two unitary vortices. An essential finding is biostability between the fundamental and vortex solitons.