Multi-structured solitons for the paraxial wave equation in a liquid crystal model

This paper focuses on the derivation of soliton solutions for the M−truncated (MTF) fractional Paraxial wave (PWE) equation emerging in a liquid crystal model employing the Generalized Riccati Equation Approach (GREA) and a novel Π ρ Π + Ω expansion approach. This equation is crucial for studying optical properties such as light transmission, diffraction, and focusing in liquid crystal devices. It likewise has a significant influence on the design and optimization of liquid crystal displays (LCDs), optical communication systems, and imaging technologies that incorporate liquid crystal materials. Furthermore, it can aid in discovering new applications in photonics and nanotechnology. We explore the impact of specific factors on the solutions of these governing equations and utilize 3D and 2D graphs to illustrate dynamic wave patterns. These findings are essential for both understanding the dynamics of the M−truncated (MTF) fractional paraxial wave (PWE) equation and applications related to NFPDE in nonlinear science.