The dynamics of a Pearcey–Gaussian (PG) beam with Gaussian potential in the fractional Schrödinger equation (FSE) are investigated. In free space, varying the Lévy index offers a convenient way to control the splitting and bending angle of the beam. In the presence of Gaussian potential, with increasing propagation distance, the process is repeated in a breath-like motion. The periodicity also can be changed by adjusting the potential parameter and incident beam arguments, such as potential height, potential width and transverse wavenumber. The transmission and reflection of the beam can also be controlled by varying the potential parameters. Moreover, when a symmetrical Gaussian potential barrier is selected, total reflection is more likely to occur. These unique characteristics demonstrate the possibility of controlling the dynamics of PG beams with the FSE system.

中文翻译：

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高斯势下分数阶薛定谔方程中 Pearcey-Gaussian 光束的周期性演化

研究了分数阶薛定谔方程 (FSE) 中具有高斯势的 Pearcey-Gaussian (PG) 光束的动力学。在自由空间中，改变 Lévy 指数提供了一种方便的方法来控制光束的分裂和弯曲角度。在存在高斯势的情况下，随着传播距离的增加，该过程以类似呼吸的运动重复进行。周期性也可以通过调整势参数和入射光束参数来改变，例如势高、势宽和横向波数。光束的透射和反射也可以通过改变电位参数来控制。此外，当选择对称的高斯势垒时，更容易发生全反射。