The generalized fractional Kundu-Mukherjee-Naskar equation (gFKMNE) is a nonlinear fractional partial differential equation (NFPDE) that models nonlinear pulse transmission in communication systems and optical fibers. This work investigates the gFKMNE in (2+1) dimensions, seeking optical soliton solutions. Using a wave transformation, the gFKMNE is converted into nonlinear ordinary differential equations (NODEs) of integer order. The modified extended direct algebraic approach is then applied to solve the NODE, yielding nonlinear algebraic equations and series-form solutions. The solutions, obtained using Maple-13, reveal optical soliton solutions for the gFKMNE. These soliton solutions can be stacked to produce black lattices in optical media, visible in contour plots and 3D photographs. These dark soliton lattices are crucial in telecommunications, optical signal processing, and nonlinear optics. Further analysis examines the influence of various parameters on soliton behavior, demonstrating that soliton solutions exhibit distinct features depending on parameters like amplitude, width, and velocity. This study showcases the effectiveness of the modified extended direct algebraic technique in solving complex NFPDEs, providing new insights into soliton behavior in optical media.
Ullah et al. (Tue,) studied this question.