  We study classical dynamics of a probe Dp-brane moving in a background
sourced by a stack of Dp-branes. In this context the physics is similar to that
of the effective action for open-string tachyon condensation, but with a
power-law runaway potential. We show that small inhomogeneous ripples of the
probe brane embedding grow with time, leading to folding of the brane as it
moves. We give a full nonlinear analytical treatment of inhomogeneous brane
dynamics, suitable for the Dirac-Born-Infeld + Wess-Zumino theory with
arbitrary runaway potential, in the case where the source branes are BPS. In
the near-horizon geometry, the inhomogeneous brane motion has a dual
description in terms of free streaming of massive relativistic test particles
originating from the initial hypersurface of the probe brane. We discuss
limitations of the effective action description around loci of self-crossing of
the probe brane (caustics). We also discuss the effect of brane folding in
application to the theory of cosmological fluctuations in string theory
inflation.
