Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.The work of O.V.Sh., M.P.F., and S.K.T. was supported by the Russian Science Foundation (Grant No. 17-72-30006). This research was also supported by the Liverhulme Trust (a visiting professorship), the Erasmus Mundus program of the European Union (NanoPhi), and the Australian National Universit