论文标题
立方分数非线性schrodinger方程的周期性驻波的轨道稳定性
Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrodinger equation
论文作者
论文摘要
在本文中，研究了具有立方非线性的非线性分数Schrodinger（FNLS）方程的周期性常规溶液的存在和轨道稳定性。存在通过在复杂环境中使用最小的约束问题来确定，我们表明相应的实际解决方案始终是正面的。轨道稳定性是通过组合一些有关正运算符的工具，分数山载算子的振荡定理和vakhitov-Kolokolov条件的，以Schrodinger方程而闻名。然后，我们使用PETVIASHVILI的迭代方法执行一种数值方法来生成FNLS方程的周期性常规解决方案。我们还从数值上研究了vakhitov-kolokolov条件，对于某些分数衍生物的某些值，无法在分析上获得。
In this paper, the existence and orbital stability of the periodic standing waves solutions for the nonlinear fractional Schrodinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and we it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding positive operators, the oscillation theorem for fractional Hill operators and a Vakhitov-Kolokolov condition, well known for Schrodinger equations. We then perform a numerical approach to generate periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.
