Reducible KAM tori for two-dimensional nonlinear Schrodinger equations with explicit dependence on the spatial variable

摘要

We study the two-dimensional nonlinear Schrodinger equation iu(t) -Delta u + |u|(2)u partial derivative integral (x, u, u )/partial derivative u = 0, t is an element of R, x is an element of T-2 with periodic boundary conditions. The nonlinearity f (x, u, u) =Sigma(j,l,j+l >= 6) a(jl)(x)u(j)u, a(jl) = a(lj) is a real analytic function 6 in a neighborhood of the origin. We obtain, through an infinite dimensional KAM theorem, a Whitney smooth family of small-amplitude quasi-periodic solutions. (c) 2022 Elsevier Inc. All rights reserved.