We extend the general solution to the Cauchy problem for the relativistic closed string (Phys. Lett. B 404 (1997) 57) 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, (C) 1998 Elsevier Science B.V. All rights reserved. [References: 16]
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