Strange attractors, nonlinear dynamics and abundant novel soliton solutions of the Akbota equation in Heisenberg ferromagnets

Abstract

The prime objective of the present investigation is to classically unveil the dynamical properties of nonlinear Akbota equation, connected with Heisenberg ferromagnets. The Akbota equation serves as a fundamental model to study the nonlinear phenomena in magnetism, optics, and more generally in the differential geometry of curves and surfaces. We accomplish this by starting with creation of dynamical system (DS) associated to the proposed model. Then, the stimuli of bifurcations in the system are investigated using the planar DS theory. Next, we systematically study that the Akbota equation exhibits chaotic phenomena by adding a perturbation term to its subsequent dynamic setting. We also verify this investigation by displaying 2D and 3D phase portraits. The Lyapunov exponents (LEs) and bifurcations maps with respect to parameters are explored. Some more novel nonlinear dynamics such as return maps, power spectrum, recurrence plot, fractal dimension, and strange novel chaotic attractors are presented. The simulation results is carried out using the RK-4 method. For several soliton solutions, the improved modified extended Tanh-function technique (IMETFT) and the method of the planar DS are applied with a detailed investigation to demonstrate a variety of solutions that the governing model can exhibit. Also, the stability analysis of solutions confirms that the solutions are stable.