This study explores optical solitons in the Biswas–Arshed equation within birefringent fibers. Employing the unified solver method, the \(\left( \frac{1}{\varphi (\eta )},\frac{\varphi '(\eta )}{\varphi (\eta )}\right)\) method, and new Kudryashov’s method, we extract various optical soliton solutions, encompassing dark, singular, bright, and periodic forms. These solutions deepen our understanding of dynamic phenomena in birefringent fibers, showcasing their potential practical applications. The results, effectively visualized in 3D and 2D plots, reveal intricate patterns. Our research underscores the efficacy and simplicity of these approaches in obtaining optical solitons for diverse nonlinear evolution equations. The novelty lies in the advanced methodologies applied to investigate the Biswas–Arshed equation, yielding a diverse array of soliton solutions and their practical implications. This study not only presents a variety of solutions but also highlights their applicability across disciplines and real-world scenarios. Consequently, our research significantly contributes to advancing our understanding of optical solitons in birefringent fibers, offering a methodological breakthrough in engineering and applied physics.
