In this paper, we introduce the fiber Bragg gratings for cubic-quartic perturbed Lakshmanan–Porsezian–Daniel equation with Kerr law nonlinearity. Two mathematical methods, namely, the modified Kudryashov’s method and the addendum to Kudryashov’s method are applied to obtain optical soliton solutions to this equation. Dark soliton, bright soliton and singular soliton solutions have been found. The comparative analysis of the two proposed methods shows that the first method gives the dark and singular solitons while the second method gives the bright and singular solitons.

中文翻译：

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Lakshmanan-Porsezian-Daniel模型在光纤布拉格光栅中的三次四次光学孤子解的两种积分方案

在本文中，我们介绍了具有Kerr律非线性的三次四阶扰动Lakshmanan–Porsezian–Daniel方程的光纤布拉格光栅。应用了两种数学方法，即改进的Kudryashov方法和Kudryashov方法的附录来获得该方程的光学孤子解。已发现暗孤子，亮孤子和奇异孤子解。对这两种方法的比较分析表明，第一种方法给出了暗和奇异的孤子，而第二种方法给出了亮和奇异的孤子。