The purpose of this note is three-fold. First, a sharp threshold of global existence versus blow-up dichotomy of solutions to some non-linear fractional coupled Schrödinger equations is investigated. Second, using the potential-well method, the existence of non global solutions is proved. Finally, instability by blow-up of mass-super-critical and energy sub-critical standing waves is obtained.

中文翻译：

---

一类分数耦合薛定ding系统的渐近性

本文的目的是三方面的。首先，研究了一些非线性分数耦合Schrödinger方程解的整体存在与爆炸二分法的尖锐阈值。其次，使用势阱方法，证明了非整体解的存在性。最后，获得了由质量超临界和能量亚临界驻波爆炸引起的不稳定性。