This study explores the intricate details of a high-order concatenation equation with cubic nonlinearity, which is crucial for understanding nonlinear Schrödinger equations. It highlights the importance of concatenation, which involves a sequence of operators vital for analyzing these equations’ behavior. The research illuminates the complex nature of nonlinear Schrödinger equations and their solitonic solutions through comprehensive examination. Investigating various operators such as Hirota, Lakshmanan–Porsezian–Daniel, and quintic, alongside advanced integration methods, including an addition to Kudryashov’s process and the unified Riccati equation approach, the study showcases their utility in real-world applications. It delves into the conditions for various bright, dark, and singular soliton types, assessing their properties. This study stands out because it analyzes a novel architecture within the dispersive concatenation model in birefringent fibers. The research is expected to significantly contribute to the advancement of polarization-maintaining fibers, which are crucial for maintaining the polarization state of light in various specialized applications. The results, enhanced by graphical representations of particular solitons, aim to push forward the field of optical fiber technology, focusing on creating materials, devices, and systems that utilize solitonic phenomena to boost communication and data processing technologies.