Pérez García, Victor M.. 

We show how to generate robust self-sustained clusters of soliton bullets—spatiotemporal (optical or matter-wave) solitons. The clusters carry an orbital angular momentum being supported by competing nonlinearities. The “atoms” forming the “molecule” are fully three-dimensional solitons linked via a staircaselike macroscopic phase. Recent progress in generating atomic-molecular coherent mixing in the Bose-Einstein condensates might open potential scenarios for the experimental generation of these soliton molecules with matter waves.