In this paper, by applying the direct method of moving planes, the authors study the radial symmetry of standing waves for nonlinear fractional Laplacian Schrödinger systems with Hardy potential. Firstly, under the condition of infinite decay, the radial symmetry of the solution is established. Secondly, under the condition of no decay, the radial symmetry and non-existence of solution are established by the Kelvin transform.

中文翻译：

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非线性分数阶Laplacian Hardy–Schrödinger系统的驻波径向对称

在本文中，通过应用直接移动平面方法，作者研究了具有Hardy势的非线性分数阶LaplacianSchrödinger系统的驻波径向对称性。首先，在无限衰减的条件下，建立了解的径向对称性。其次，在不衰减的条件下，通过开尔文变换建立了径向对称性和解的不存在性。