本项目以非线性Schrödinger方程为模型，从动力学角度出发，拟围绕其拟周期解的存在性问题展开研究。非线性Schrödinger方程是数学物理中最著名和最重要的非线性发展方程之一，可以用来描述非线性光学、等离子物理、通信等许多领域中的非线性现象，其周期解及拟周期解的存在性问题是当今数学物理领域备受关注的热点问题之一。. 本项目旨在发展Lyapunov-Schmidt约化和Nash-Moser迭代方法,研究非线性Schrödinger方程拟周期解的存在性。拟周期结构反映了各向异性的性质。本项目的创新之处在于所研究的是一个无界摄动问题，并且非线性项中含有与方程最高阶导数同阶的项。通过这些研究,有助于理解非线性Schrödinger方程的动力学机制,为分析和解决实际问题提供理论依据和研究方法。

From the perspective of dynamics,this project takes nonlinear Schrödinger equation as the model, and intends to study the existence of its quasi-periodic solutions. Nonlinear Schrödinger equation is one of the most famous and important nonlinear evolution equations in mathematical physics. It can be used to describe many nonlinear phenomena in many fields such as nonlinear optics, plasma physics, communications, and so on. The problem of the existence of its periodic solutions and quasi-periodic solutions has become one of the hot issues in the field of mathematical physics..This project aims to develop Lyapunov-Schmidt reduction and Nash-Moser iterative methods, and to study the existence of quasi-periodic solutions of nonlinear Schrödinger equations. The quasi-periodic structure reflects the property of anisotropy. The innovation of this project lies in that we’ll study a problem of unbounded perturbation, and the nonlinear terms contain the same order terms as the highest-order derivative of the equation. These studies will help to understand the dynamic mechanism of nonlinear Schrödinger equation, and provide theoretical basis and research methods for analyzing and solving practical problems.