Abstract : We study the initial value problem of the exponential wave equation in $\mathbb{R }^{n+1}$ for small initial data. We shows, in the case of $n = 1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n\geq 2$, a vector field method is applied to show the stability of a trivial solution $\phi=0$.
Keywords : quasilinear wave, weakly linearly degenerate, double null form
