A KAM algorithm for two-dimensional nonlinear Schr?dinger equations with spatial variable

We consider the two-dimensional nonlinear Schrodinger equation [GRAPHICS.] with periodic boundary conditions, where the nonlinearity H(x, u, (u) over bar) = Sigma(infinity)(m=1)alpha m(x)|u|(2p+2m) u is a real analytic function in a neighborhood of the origin. We obtain, through a KAM algorithm, a Whitney smooth family of small-amplitude quasi-periodic solutions. (c) 2023 Elsevier Inc. All rights reserved.