Analysis of Lie-Bäcklund symmetry soliton solutions and stability dynamics in the Wazwaz unidirectional wave model

This work present comprehensive analysis of the Wazwaz Unidirectional Wave Model (UWM) to explore ultra-short pulse propagation in silica optical fibers. By determining the Lie-Bäcklund symmetry group and employing the multiplier method, infinite conservation laws are derived, underscoring the model's integrability. Soliton solutions are obtained using the sine-Gordon expansion approach (SGEA) and compared with earlier solutions to highlight consistency and accuracy. Additionally, the stability of the solutions is validated through stability analysis. The novelty of this work lies in the comprehensive integration of symmetry, conservation, and stability analyses, which advances previous efforts by offering a holistic understanding of the model's properties and providing a foundation for future theoretical and applied studies.