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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.
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Thawatchai Mayteevarunyoo, Boris A. Malomed, Dmitry V. Skrybin, "Spatiotemporal solitons and vortices in graded-index multimode lossy fibers," Proc. SPIE 11331, Fourth International Conference on Photonics Solutions (ICPS2019), 113310W (11 March 2020); https://doi.org/10.1117/12.2551842