Constructing optical soliton wave structure and modulation instability analysis for coupled fractional Lakshmanan-Porsezian-Daniel equation with Kerr’s law nonlinearity

In this paper, the optical soliton wave structure and other types of soliton solutions are investigated. The coupled fractional Lakshmanan-Porsezian-Daniel equation explains the wave pulses' physical features in optical fibres along with two vector solitons. The Jacobi elliptic function expansion scheme is utilized to find various kinds of optical solitons. This scheme is among the most powerful techniques for creating numerous exact solutions for different nonlinear partial differential equations. Also, the generalized [Formula: see text]-expansion method is used to get the exact solutions. Firstly, the wave transform converts the considered equations into nonlinear ordinary differential equations. Then, the new exact solutions are developed as periodic, dark, combined hyperbolic, and rational form functions. By employing the symbolic computation to the mentioned scheme the obtained solutions are investigated. The coupled fractional Lakshmanan-Porsezian-Daniel model is analyzed because of density plot and two-dimensional plot. The modulation instability analysis is investigated. It offers theoretical application value for the study of complex wave dynamics in various scientific domains, such as fluid dynamics, plasma physics, and nonlinear optics.