New optical soliton solutions to the coupled fractional Lakshmanan–Porsezian–Daniel equations with Kerr law of nonlinearity

This article studies the optical soliton solutions of the coupled fractional Lakshmanan–Porsezian–Daniel equations with kerr’s law nonlinearity based on the complete discriminant system of cubic polynomials. By means of traveling wave transformation, the fractional Lakshmanan–Porsezian–Daniel equations are simplified into two ordinary differential equations. Then, according to the classification of the roots of cubic polynomials, the optical soliton solutions of the fractional model with Kerr’s law nonlinearity are traversed. Then new traveling wave solutions are obtained, including the rational solutions, triangle function solutions, implicit function solutions and Jacobian elliptic function solutions, and the corresponding solutions are shown in two-dimensional and three-dimensional figures. Compared with previous related research, the exact optical soliton solutions of the LPD equation system for nonlinear Kerr’s law presented in this study are more completely and clearly classified, and researchers are easier to obtain these solutions