Quasi-Periodic solutions of Two Dimensional Completely Resonant Reversible Schrödinger d Systems

We introduce an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible Schrödinger systems. Using this KAM theorem together with partial Birkhoff normal form method, we find the existence of quasi-periodic solutions for a class of completely resonant reversible coupled nonlinear Schrödinger d systems on two dimensional torus.