  We unveil the dynamical formation of multiple localized structures in the
form of dark-bright and dark-antidark solitary waves that emerge upon quenching
a one-dimensional particle-imbalanced Bose-Bose mixture. Interspecies
interaction quenches drive the system out-of-equilibrium while the so-called
miscible/immiscible threshold is crossed in a two directional manner.
Dark-bright entities are spontaneously generated for quenches towards the phase
separated regime and dark-antidark states are formed in the reverse process.
The distinct mechanisms of creation of the aforementioned states are discussed
in detail and their controlled generation is showcased. In both processes, it
is found that the number of solitary waves generated is larger for larger
particle imbalances, a result that is enhanced for stronger postquench
interspecies interactions. Additionally the confining geometry highly affects
the production of both types of states with a decaying solitary wave formation
occurring for tighter traps. Furthermore, in both of the aforementioned
transitions, the breathing frequencies measured for the species differ
significantly for highly imbalanced mixtures. Finally, the robustness of the
dynamical formation of dark-bright and dark-antidark solitons is also
demonstrated in quasi one-dimensional setups.
