Bounded Sobolev norms for Klein-Gordon equations under non-resonant perturbation
Bounded Sobolev norms for Klein-Gordon equations under non-resonant perturbation
In this paper, we prove Anderson localization for the Klein-Gordon operator on the circle 𝕋 under non-resonant perturbations. Furthermore, using the result, we show that the Sobolev norms of solutions to the corresponding Klein-Gordon equations remain bounded for all time.