  We investigate the quench dynamics of a two-component Bose mixture and study
the onset of modulational instability, which leads the system far from
equilibrium. Analogous to the single-component counterpart, this phenomenon
results in the creation of trains of bright solitons. We provide an analytical
estimate of the number of solitons at long times after the quench for each of
the two components based on the most unstable mode of the Bogoliubov spectrum,
which agrees well with our simulations for quenches to the weak attractive
regime when the two components possess equal intraspecies interactions and loss
rates. We also explain the significantly different soliton dynamics in a
realistic experimental homonuclear potassium mixture in terms of different
intraspecies interaction and loss rates. We investigate the quench dynamics of
the particle number of each component estimating the characteristic time for
the appearance of modulational instability for a variety of interaction
strengths and loss rates. Finally, we evaluate the influence of the
beyond-mean-field contribution, which is crucial for the ground-state
properties of the mixture, in the quench dynamics for both the evolution of the
particle number and the radial width of the mixture. In particular, even for
quenches to strongly attractive effective interactions, we do not observe the
dynamical formation of solitonic droplets.
