Motivated by work in nonlinear optics, as well as more recently
in Bose-Einstein condensate mixtures, we will explore a
series of nonlinear states that arise in such systems. We
will start from a single structure, the so-called dark-bright solitary wave, and then
expand our considerations to multiple such waves, their
spectral properties, nonlinear interactions and experimental
observations. A twist will be to consider the dark
solitons of the one component as effective potentials that will trap the bright
