Quasi-periodic solutions of Schrödinger equations with quasi-periodic forcing in higher dimensional spaces
نویسندگان
چکیده
In this paper, d-dimensional (dD) quasi-periodically forced nonlinear Schrödinger equation with a general nonlinearity iut −∆u+Mξu+ εφ(t)(u+ h(|u| 2)u) = 0, x ∈ T, t ∈ R under periodic boundary conditions is studied, where Mξ is a real Fourier multiplier and ε is a small positive parameter, φ(t) is a real analytic quasi-periodic function in t with frequency vector ω = (ω1,ω2 . . . ,ωm), and h(|u| 2) is a real analytic function near u = 0 with h(0) = 0. It is shown that, under suitable hypothesis on φ(t), there are many quasi-periodic solutions for the above equation via KAM theory. c ©2017 All rights reserved.
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