  We study the black string solutions in the Einstein-Gauss-Bonnet(EGB) theory
at large $D$. By using the $1/D$ expansion in the near horizon region we derive
the effective equations that describe the dynamics of the EGB black strings.
The uniform and non-uniform black strings are obtained as the static solutions
of the effective equations. From the perturbation analysis of the effective
equations, we find that thin EGB black strings suffer from the Gregory-Laflamme
instablity and the GB term weakens the instability when the GB coefficient is
small, however, when the GB coefficient is large the GB term enhances the
instability. Furthermore, we numerically solve the effective equations to study
the non-linear instability. It turns out that the thin black strings are
unstable to developing inhomogeneities along their length, and at late times
they asymptote to the stable non-uniform black strings. The behavior is
qualitatively similar to the case in the Einstein gravity. Compared with the
black string instability in the Einstein gravity at large D, when the GB
coefficient is small the time needed to reach to final state increases, but
when the GB coefficient is large the time to reach to final state decreases.
Starting from the point of view in which the effective equations can be
interpreted as the equations for the dynamical fluid, we evaluate the transport
coefficients and find that the ratio of the shear viscosity and the entropy
density agrees with that obtained previously in the membrane paradigm after
taking the large $D$ limit.
