Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility

Athanasios Chatzikaleas, Jacques Smulevici

Given any wave operator with principle part ${\partial }_t^2-{\partial }_x^2+{\mathcal{B}}^{xx}(\omega t,x){\partial }_x^2$, where ${\mathcal{B}}^{xx}:{\mathbb{T}}^{\nu +1}\to \mathbb{R}$…