  We derive a simple set of non-linear, (1+1)-dimensional partial differential
equations that describe the dynamical evolution of black strings and branes to
leading order in the expansion in the inverse of the number of dimensions D.
These equations are easily solved numerically. Their solution shows that thin
enough black strings are unstable to developing inhomogeneities along their
length, and at late times they asymptote to stable non-uniform black strings.
This proves an earlier conjecture about the endpoint of the instability of
black strings in a large enough number of dimensions. If the initial black
string is very thin, the final configuration is highly non-uniform and
resembles a periodic array of localized black holes joined by short necks. We
also present the equations that describe the non-linear dynamics of
Anti-deSitter black branes at large D.
