Dynamic investigation of the Laksmanan–Porsezian–Daniel model with Kerr, parabolic, and anti-cubic laws of nonlinearities

The Laksmanan–Porsezian–Daniel model is one of the useful models used in nonlinear optics. The extended G ′ G 2 -expansion method is used to discuss the dynamical behavior of the proposed model. Many novel solitary wave solutions are obtained using the considered model. To deal with the nonlinearity of this model, three laws of nonlinearity are used, namely, Kerr law, parabolic law, and anti-cubic law. Three-dimensional surface, two-dimensional contour, density, and two-dimensional-line plots of some retrieved solutions are drawn using Maple software. The graphical simulations show the shape and structure of the wave profile corresponding to the obtained results.