We explore various self-trapped states, including sharp matter-wave solitons and spatially broad self-bound droplets (SBDs), in an effectively one-dimensional atomic-molecular bosonic-condensate mixture (unlike the well-known mechanism of the formation of quantum droplets in atomic Bose-Einstein condensates, in the present system SBDs are produced without the action of the beyond-mean-field effects). The analysis reveals a transition between the solitons and SBDs, passing through a self-bound hybrid state (SBHS). When the intermolecular interaction is switched off, the system exhibits a soliton state with low values of the scaled number of particles (alias the total norm), $N$. The system transitions to the SBHS as $N$ increases. In the hybrid regime, both the maximum density and spatial size of the state grow with $N$, while the chemical potential decreases. The SBHS family is described, in an analytical form, by the “cascading-limit approximation,” which is suggested by the similarity to the optical second-harmonic-generating system. A phase diagram in the $(g,N)$ plane is constructed, and the Bogoliubov–de Gennes analysis, together with real-time simulations, confirms the stability of all three types of self-bound states in their respective parameter regimes. Simulations demonstrate that collisions between the bound states are inelastic, featuring fusion or fragmentation, depending on the collision speed.

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• Solitons