Almost periodic solutions for a class of higher dimensional Schrödinger equations

Abstract

In this paper, we show that there are almost periodic solutions corresponding to full dimensional invariant tori for higher dimensional Schrödinger equations with Fourier multiplier iu_t −Δu+M_ξu+f(|u|²)u = 0, subject to periodic boundary conditions, where the nonlinearity f is a real-analytic function near u = 0 with f(0) = 0. The proof is based on an improved infinite dimensional KAM theorem.

Keywords

Schrodinger equation / almost-periodic solution / KAM method

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