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Stable Spinning Optical Solitons in Three Dimensions
We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr\"odinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing …