Study of magnetic fields using dynamical patterns and sensitivity analysis

The exploration of the nonlinear dynamics related to the new coupled Konno–Oono equation, which determines the propagation of magnetic fields, is the focus of this work. Through the employing of Lie group analysis, the bifurcation phase portraits, and chaos theory, the project will investigate symmetry reductions in dynamical systems and examine the dynamic behavior of perturbed dynamical systems. The 3D phase portrait, 2D phase portrait, Lyapunov exponent, time series analysis, sensitivity analysis, and an examination of the existence of multistability in the autonomous system under various initial conditions constitute a few of the methods used for recognizing chaotic behavior. Furthermore, the investigation constructs general solutions for solitary wave solutions, such as exponential and hyperbolic function, singular, dark, and bright soliton solutions, by using the new Kudryashov methodology to determine the investigated equation analytically. These solutions are shown graphically as 2D, 3D, and contour plots with specifically selected values. They include as well with the related constraint circumstances. Additionally, a discussion and a visual illustration of the considered equation’s sensitivity analysis are presented. The observations demonstrate that the aforementioned approach is an effective procedure for treating a variety of nonlinear PDE systems that arise in nonlinear physics analytically. The plot of the Lyapunov exponents is employed to validate the chaotic dynamics of the studied model. Additionally, the multiplier method is employed to determine the conserved vectors for the analyzed problem.