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

Uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space