Invariant tori for two-dimensional nonlinear Schrödinger equations with large forcing terms

We prove an infinite dimensional Kolmogorov–Arnold–Moser theorem. As an application, we use the theorem to study the two-dimensional forced nonlinear Schrödinger equation with periodic boundary conditions, and we emphasize that the forced term is not small perturbation. We obtain a Whitney smooth family of small-amplitude quasiperiodic solutions which are partially hyperbolic.