  There is a few results about the global stability of nontrivial solutions to
quasilinear wave equations. In this paper we are concerned with the uniqueness
and stability of traveling waves to the time-like extremal hypersurface in
Minkowski space. Firstly, we can get the existence and uniqueness of traveling
wave solutions to the time-like extremal hypersurface in R1+(n+1), which can be
considered as the generalized Bernstein theorem in Minkowski space.
Furthermore, we also get the stability of traveling wave solutions with speed
of light to time-like extremal hypersurface in 1 + (2 + 1) dimensional
Minkowski space.
