Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method

In this paper, the dynamical system bifurcation theory approach are employed to investigate the phase diagrams of the magnet-optic wave guides in Kuralay. With the use of the complete discrimination system, we obtain some new traveling wave solutions, including kink solitary, convex-periodic, Jacobian elliptic function solutions, dark-soliton and implicit analytical solutions. More details about the physical dynamical representation of the presented solutions are illustrated with profile pictures. We use Mathematica and Maple to plot three-dimensional diagrams, contour plots and two-dimensional diagrams to obtain complete configurations. This paper show that the fully discriminative system approach is simple and efficient method to reach the various type of the soliton solutions, provide a more powerful mathematical tool to solve many other nonlinear partial differential equations with the help of symbolic computation and computers.