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

• Published in: Qualitative theory of dynamical systems Vol. 23; no. 3
• Main Authors: Liu, Jing, Li, Zhao
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.07.2024; Springer Nature B.V
• Subjects: Bifurcation theory; Difference and Functional Equations; Dynamical systems; Dynamical Systems and Ergodic Theory; Exact solutions; Jacobian elliptic functions; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Partial differential equations; Phase diagrams; Solitary waves; Systems analysis; Traveling waves; Waveguides; Kuralay equation; Dynamical system bifurcation theory; Complete discrimination system; Solitons
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-024-00990-5

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.