  We extend the general solution to the Cauchy problem for the relativistic
closed string (Phys. Lett. B404 (1997) 57-65, hep-th/9704084) to the case of
open strings attached to Dp-branes, including the cases where the initial data
has a knotlike topology. We use this extended solution to derive intrinsic
dynamical properties of open and closed relativistic strings attached to
Dp-branes. We also study the singularity structure and the oscillating periods
of this extended solution.
