In this work, we demonstrate the extraction of some optical soliton solutions of the Chen–Lee–Liu equation (CLLE) with applications in optical fibers. A novel method is presented which is called the new extended direct algebraic method (EDAM). This method is based on converting the nonlinear CLLE equation into an ordinary type equation through a wave transformation. We acquire new solutions like dark, bright, combined dark-bright, combined bright-singular and periodic singular soliton solutions by using this effective technique. These acquired soliton solutions are new with some new physical properties. Some graphical representations for these solutions are provided which prove that the new method is effective and can be extended to some similar problems.

中文翻译：

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Chen-Lee-Liu 方程的新光孤子解

在这项工作中，我们展示了 Chen-Lee-Liu 方程 (CLLE) 的一些光孤子解的提取以及在光纤中的应用。提出了一种新的方法，称为新的扩展直接代数方法（EDAM）。该方法基于通过波变换将非线性CLLE方程转换为普通型方程。通过使用这种有效的技术，我们获得了新的解决方案，如暗、亮、组合暗亮、组合亮奇异和周期性奇异孤子解。这些获得的孤子解决方案是新的，具有一些新的物理特性。提供了这些解决方案的一些图形表示，证明了新方法是有效的，并且可以扩展到一些类似的问题。