Bifurcation, Phase Portrait and Traveling Wave Solutions of the Coupled Fractional Lakshmanan–Porsezian–Daniel Equation

In this paper, we investigate the bifurcation, phase portrait and the traveling wave solutions of the coupled fractional Lakshmanan–Porsezian–Daniel equation by using the dynamical system bifurcation theory approach. Based on phase portrait, we obtain some new traveling wave solutions, which include Jacobi elliptic function solutions, soliton solutions, torsion wave solutions and periodic wave solutions. What’s more, we plot three-dimensional diagrams, contour plots and two-dimensional diagrams with the help of Maple, which provide a more visual demonstration of the section of this equation. The investigations are innovative and unexplored, and they can be employed to elucidate the physical phenomena that have been simulated, providing insights into their transient dynamic characteristics.