Global stability for a nonlinear system of anisotropic wave equations

In this paper, we initiate the study of global stability for anisotropic systems quasilinear wave equations. Equations kind arise naturally in crystal optics, and they exhibit birefringence. We introduce a physical space strategy based on bilinear energy estimates that allows us to prove decay nonlinear problem. This uses homogeneous equation as black box. The proof also requires interface with vector field method take advantage scaling field. A careful analysis spacetime geometry interaction between waves is necessary proof.