Quasi-periodic solutions of two dimensional Schrödinger equations with Quasi-periodic forcing

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• 作者：Min Zhang ^{zhangminmath@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35L05 ; 37K50 ; 58E05
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：135
• 期：Complete
• 页码：1-34
• 全文大小：751 K

文摘

This work focuses on two-dimensional (2D)$\left(2D\right)$ quasi-periodically forced nonlinear Schrödinger equations. This means studying with periodic boundary conditions, where ε$\epsilon$ is a small positive parameter, ϕ(t)$\varphi \left(t\right)$ is a real analytic quasi-periodic function in t$t$ with frequency vector ω=(ω₁,ω₂…,ω_m)$\omega =({\omega }_1,{\omega }_2\dots ,{\omega }_m)$. It is shown that, under suitable hypothesis on ϕ(t)$\varphi \left(t\right)$, there are many quasi-periodic solutions for the above equation via KAM theory.