非线性离散系统的周期解和同宿解

项目名称： 非线性离散系统的周期解和同宿解

项目编号： No.11526056

项目类型： 专项基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 黄梅华

作者单位： 广东财经大学

项目金额： 3万元

中文摘要： 首先，利用 Nehari 流形结合周期逼近的方法讨论了耦合离散非线性薛定谔方程两类基态解的存在性，一类为周期基态解；一类为同宿基态解.其次，得到同宿基态解的各个分量均不为零. 最后，利用数值方法模拟耦合离散非线性薛定谔方程（具有三分量）的非平凡同宿基态解.

中文关键词： 周期解；基态解；Nehari 流形；周期逼近；

英文摘要： We demonstrate the existence of ground state solutions in coupled discrete nonlinear Schr？dinger equations (CDNLS) with periodic potentials. First, we consider two types of solutions to CDNLS periodic and vanishing at infinity. Calculus of variations and the Nehari manifolds are employed to establish the existence of the periodic solutions, and then, using periodic approximations, we present sufficient conditions on the existence of ground state solutions which are vanishing at infinity. Second, we show that each of the components of this ground state solutions are not zero. Third, extensive numerical examples in three dimensions for ground state solutions are presented to demonstrate the power of the numerical methods.

英文关键词： Periodic solutions；Ground state solution；Nehari manifold；Periodic approximation；