  We explore the stability and dynamics of dark-bright solitons in
two-component elongated Bose-Einstein condensates by developing effective 1D
vector equations as well as solving the corresponding 3D Gross-Pitaevskii
equations. A strong dependence of the oscillation frequency and of the
stability of the dark-bright (DB) soliton on the atom number of its components
is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the
transverse degrees of freedom for a large occupation of the component
supporting the dark soliton. Moreover, the interactions of two DB solitons are
investigated with special emphasis on the importance of their relative phases.
Experimental results showcasing dark-bright soliton dynamics and collisions in
a BEC consisting of two hyperfine states of $^{87}$Rb confined in an elongated
optical dipole trap are presented.
