Abstract: We consider the initial-boundary value problems on $\mathbb{R}^{+}\times \mathbb{R}^{+}$ for one-dimension systems of quasilinear wave equations with null conditions. We first show that for homogeneous Dirichlet boundary values and sufficiently small initial data, classical solutions always globally exist. Then we prove that the global solution will scatter, i.e., it will converge to some solution of one dimensional homogeneous linear wave equations as time tends to infinity, in the energy sense. Finally we show the inverse scattering result: the scattering data can determine the global solution uniquely.

Key words: one-dimension quasilinear wave equations, null condition, global existence, scattering, inverse scattering