基于分数阶薛定谔方程，研究了对称皮尔斯脉冲的传输特性。研究发现，在Lévy指数作用下，对称皮尔斯脉冲劈裂为强度相等的两束光。当Lévy指数等于1时，两束皮尔斯脉冲能够保持较长距离的稳定传输。随后引入变系数，在周期调制的作用下，对称皮尔斯脉冲在传输过程中发生周期性聚焦，脉冲特性在焦点处重现且强度基本维持不变。其次，讨论了Lévy指数和啁啾参数对皮尔斯脉冲传输特性的影响。结果表明，对于具有二次啁啾的皮尔斯脉冲，Lévy指数与啁啾参数会影响焦点处的强度。啁啾参数保持不变，Lévy指数越大，焦点处强度越大。Lévy指数保持不变，啁啾参数绝对值越大，焦点处强度越大。此外，不同参数对皮尔斯脉冲相互作用的影响也进行了研究。改变脉冲的间距，相位，焦点位置处的强度也会发生相应的变化。

Based on fractional Schrödinger equation with variable coefficient, the transmission characteristics of symmetric Pearcey pulse are studied. When the variable coefficient is not considered, it is found that under the action of Lévy index, the symmetric Pearcey pulse splits into two pulses of equal intensity. Especially, when Lévy index equals one, the two Pearcey pulses can maintain the stable transmission over a long distance. When the variable coefficient is considered, under the action of periodic modulation, the symmetric pulse is periodically focused during transmission. The pulse is reshaped at the focal point and the intensity remains basically unchanged. Secondly, the influence of Lévy index and chirp parameter on the transmission characteristics of Pearcey pulse is discussed. The results show that the pulse intensity at the focal point can be controlled by Lévy index and the chirp parameter. The larger the Lévy index, the greater the intensity at the focus. Similarly, the larger the absolute value of the chirp, the greater the intensity at the focus. In addition, the influence of different parameters on the Pearcey pulse interaction is also studied. The change of the pulse spacing and phase, pulse intensity at the focus will also change accordingly.