  We propose a method to obtain a manifestly supersymmetric action functional
for interacting brane systems. It is based on the induced map of the
worldvolume of low-dimensional branes into the worldvolume of the space-time
filling brane ((D-1)-brane), which may be either dynamical or auxiliary, and
implies an identification of Grassmann coordinate fields of lower dimensional
branes with an image of the Grassmann coordinate fields of that (D-1)-brane.
With this identification the covariant current distribution forms with support
on the superbrane worldvolumes become invariant under the target space
supersymmetry and can be used to write the coupled superbrane action as an
integral over the D-dimensional manifolds ((D-1)-brane worldvolume). We compare
the equations derived from this new ('Goldstone fermion embedded') action with
the ones produced by a more straightforward generalization of the free brane
actions based on the incorporation of the boundary terms with Lagrange
multipliers ('superspace embedded' action). We find that both procedures
produce the same equations of motion and thus justify each other. Both actions
are presented explicitly for the coupled system of a D=10 super-D3-brane and a
fundamental superstring which ends on the super-D3-brane.
