Novel Optical Solitary Wave Structure Solution of Lakshmanan-Porsezian-Daniel Model

The Lakshmanan-Porsezian-Daniel (LPD) model, an extended version of the nonlinear Schro center dot dinger equation, plays a crucial role in comprehending optical solitons-self-reinforcing waves that maintain their form while traveling through a medium. This study employed the G2 -expansion method to explore the model and present new exact solitary wave solutions with various nonlinearities, including the Kerr, anti-cubic, and parabolic laws. The findings provide solutions for different types of optical solitons, such as bright solitons, dark solitons, rational functions, and periodic solitons. The obtained results offer fresh insights into the complex LPD model, deepening our core understanding of optical soliton dynamics. Importantly, these findings have significant implications for soliton-based applications, specifically in modern communication networks and nonlinear optics, directly impacting optical fiber transmission. Furthermore, the research introduces singular solitons, a unique and highly localized wave phenomenon, through an influential and systematic approach to exact optical solutions for various models. As communication technology and nonlinear optics continue to advance, these findings hold substantial promise for practical applications in the development of cutting-edge optical devices and systems.