We derive a family of optical solitons from a non-linear Schrdinger’s equation with an external potential in a (1 + 1)D system. The soliton solutions can be expressed in a closed form by using a Lorentzian apodization and associated Legendre functions, in contrast to the more common solitons using a Gaussian apodization. Similarly, an analytical and bounded form for the external optical potential is also found, and furthermore, a general formula for the power is obtained. Remarkably, we found that these solitons are stable in their propagation for certain values of power and width of the solitons. Finally, we report several interesting propagation dynamics for the unstable scenario: from loss of the beam’s inner structure by splitting of the initial soliton profile to breathing decaying solitons.

我们从 (1 + 1)D 系统中具有外部电位的非线性薛定谔方程推导出了一系列光学孤子。与使用高斯切趾的更常见孤子相比，孤子解可以通过使用洛伦兹切趾和相关的勒让德函数以封闭形式表示。类似地，还找到了外光势的解析和有界形式，并进一步得到了功率的通式。值得注意的是，我们发现这些孤子在某些功率和孤子宽度值的传播中是稳定的。最后，我们报告了不稳定情况下的几个有趣的传播动力学：从初始孤子轮廓分裂导致的光束内部结构损失到呼吸衰减孤子。