Quasi-periodic solutions for nonlinear wave equations (announcement)

We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This generalizes the method developed in the limit-elliptic setting of NLS to the hyperbolic setting. The additional ingredient is a Diophantine property of algebraic numbers.