  We report on the existence and stability of multidimensional bound solitonic
states in harmonically-trapped scalar Bose-Einstein condensates. Their
equilibrium separation, as a measure of the strength of the soliton-soliton or
the solitonic vortex-vortex interaction, is provided for varying chemical
potential $\mu$. Static bound dark solitons are shown to be dynamically stable
in elongated condensates within a range of intermediate (repulsive)
interparticle-interaction strength. Beyond this range the snaking instability
manifests during the time evolution of the planar solitons and produces the
decay into non-stationary vortex states. A subsequent dynamical recurrence of
solitons and vortices can be observed at low $\mu$. At equilibrium, the
bifurcations of bound dark solitons are bound solitonic vortices. Among them,
both two-open and two-ring vortex lines are demonstrated to exist with both
counter- and co-rotating steady velocity fields. The latter flow configurations
evolve, for high chemical potential, into a stationary 3D-chain-shaped vortex
and a three vortex-antivortex-vortex ring sequence that arrest the otherwise
increasing angular or linear momentum respectively. As a common feature to the
bifurcated vortex states, their excitation spectra present unstable modes with
associated oscillatory dynamics.
