非线性离散系统的周期解和同宿解

We demonstrate the existence of ground state solutions in coupled discrete nonlinear Schrödinger 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.

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.