  We introduce a model for spatiotemporal modelocking in multimode fiber
lasers, which is based on the (3+1)-dimensional cubic-quintic complex
Ginzburg-Landau equation (cGLE) with conservative and dissipative
nonlinearities and a 2-dimensional transverse trapping potential. Systematic
numerical analysis reveals a variety of stable nonlinear 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. A characteristic
feature of the system is bistability between the fundamental and vortex
spatiotemporal solitons.
