KAM 理论是研究具有哈密顿结构的偏微分方程拟周期解的有效方法，是处理小除数问题和保守系统扰动问题的有力工具。本项目主要研究在量子力学中有着广泛应用的非线性Schroding方程拟周期解的存在性。主要讨论非线性边界条件下，Schroding方程以及具有拟周期外力作用的 Schroding方程拟周期解的存在性。由于受非线性边界条件的影响，问题变的相当复杂。我们通过变量替换，把问题转化为在Dirichlet边界条件下，高阶导数未被完全解出（无界扰动）的Schrodinger方程的拟周期解问题。主要利用Nash-Moser硬隐函数定理以及KAM理论来证明拟周期解的存在性。

KAM theory is an effective method to study the quasi periodic solutions of partial differential equations with Hamilton structure，and， it is a powerful tool to disturbance small divisor problem and conservative system. In this project, we study the quasi periodic solutions of nonlinear Schrodinger equation which is widely used in quantum mechanics. We discuss the existence of quasi periodic solutions of Schrodinger equation and Schrodinger equation with quasi periodic forcing potential under nonlinear boundary conditions. The nonlinear boundary conditions, which makes the problem more complicated. By transformation, the problem can be changed into a quasi periodic solution of the Schrodinger equation under the Dirichlet boundary condition, which is not fully solved by the higher order derivatives (unbounded perturbation ). In this project, we prove the existence of quasi periodic solutions by using Nash-Moser hard implicit function theorem and KAM method.