Recently, solutions of the Born-Infeld theory representing strings ema
nating from a Dirichlet p-brane have been constructed, We discuss the
embedding of these Born-Infeld solutions into the non-abelian theory a
ppropriate to multiple overlapping p-branes. We also prove supersymmet
ry of the solutions explicitly in the full non-linear theory. We then
study transverse fluctuations, both from the world-brane point of view
and by analyzing a test string in the supergravity background of a Dp
-brane. We find agreement between the two approaches for the cases p =
3,4. (C) 1998 Elsevier Science B.V.