Bifurcation, Phase Portrait and Traveling Wave Solution of Aizhan–Gudekli–Nurshuak–Zhanbota Equation

This paper investigates the bifurcation, phase portrait, and traveling wave solutions of the Aizhan–Gudekli–Nurshuak–Zhanbota equation. By performing a simple linear transformation on the solution of the equation and applying the traveling wave transformation, the original equations are reduced to a system of ordinary differential equations. Through a qualitative analysis of the resulting two-dimensional dynamical system, the types and stability of equilibrium points are classified under various parameter conditions. Using both the dynamical system method and the complete discriminant system, multiple families of exact traveling wave solutions including solitary, kink, and periodic wave solutions are derived for different parameter ranges. Numerical simulations using Maple software are performed to visualize selected solutions. The obtained solutions are novel and provide a theoretical foundation for understanding the physical applications of the equation.