Bifurcation and optical solutions of the higher order nonlinear Schrödinger equation

In this paper, we employ the bifurcation to predict and construct the exact solutions of the higher order nonlinear Schrödinger equation (NLSE). We proceed to discussing the bifurcation of phase portraits and we obtain the general solutions of the higher order equation using only analytical approach. We productively achieve exact solutions involving parameters such as hyperbolic solution, Jacobi elliptic function (JEF) and dark soliton which are novel solutions. In addition, we also plot the 3D surface of some solutions obtained and provide some interpretations. It is acknowledged that the method employed here offers a more esteemed mathematical instrument for acquiring analytical answers to several nonlinear equations.