Xiaoping Yuan

Quasi-periodic solutions of nonlinear Schrödinger equations of higher dimension☆

Abstract It is shown that there are plenty of quasi-periodic solutions of nonlinear Schrodinger equations of higher spatial dimension, where the dimension of the frequency vectors of the quasi-periodic solutions are equal to that of the space.

Anderson localization for the almost Mathieu operator in the exponential regime

For the almost Mathieu operator

Quasiperiodic solutions for the cubic complex Ginzburg–Landau equation

(H_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+2\lambda \cos2\pi(\theta+n\alpha)u_n

Spectral gaps of almost Mathieu operators in the exponential regime

, Avila and Jitomirskaya guess that for a.e.

Stability of KAM tori for nonlinear Schrödinger equation

\theta

Anderson localization for the completely resonant phases

,

Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime

H_{\lambda,\alpha,\theta}

Quasi-periodic solutions of completely resonant nonlinear wave equations

satisfies Anderson localization if

Invariant Tori of Duffing-Type Equations

|\lambda| > e^{ \beta}

KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions

, and they establish this for