  Quantum droplets are ultradilute liquid states which emerge from the
competitive interplay of two Hamiltonian terms, the mean-field energy and
beyond-mean-field correction, in a weakly interacting binary Bose gas. We
relate the formation of droplets in symmetric and asymmetric two-component
one-dimensional boson systems to the modulational instability of a spatially
uniform state driven by the beyond-mean-field term. Asymmetry between the
components may be caused by their unequal populations or unequal
intra-component interaction strengths. Stability of both symmetric and
asymmetric droplets is investigated. Robustness of the symmetric solutions
against symmetry-breaking perturbations is confirmed.
