In this work, we study the collision of two and three Gaussian wave-packets in the fractional quantum mechanics platform. For this purpose, we study the effects of different parameters such as fractionality, nonlinear interactions, delta potential barrier height, and position, etc. on two and three wave-packet collision phenomena. We have used the split-step finite difference method to solve the space fractional Schrodinger equation. We have discussed the conditions lead to (A) wave-packet fission, (B) wave-packet fusion and (C) larger amplitude pulse generation through an inelastic collision of wave-packets. For these purposes, we have placed a defect in front of the colliding wave-packets. However, against the supercontinuum generation, we do not require huge values of nonlinearity. Besides, we have provided a phase diagram that determines the allowed defect strength and fractionality strength α to have the wave-packet fusion or fission conditions.

中文翻译：

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分数阶薛定谔方程中的非平凡波包碰撞和展宽 形式主义

在这项工作中，我们研究了分数量子力学平台中两个和三个高斯波包的碰撞。为此，我们研究了不同参数，如分数、非线性相互作用、δ 势垒高度和位置等对两个和三个波包碰撞现象的影响。我们使用分步有限差分法求解空间分数阶薛定谔方程。我们已经讨论了导致 (A) 波包裂变、(B) 波包融合和 (C) 通过波包的非弹性碰撞产生更大幅度脉冲的条件。为了这些目的，我们在碰撞波包的前面放置了一个缺陷。然而，对于超连续谱的产生，我们不需要巨大的非线性值。除了，