The generalized soliton wave structures and propagation visualization for Akbota equation

Abstract This paper explores in detail the integrable Akbota equation, a Heisenberg ferromagnet-type problem that is essential to the study of surface and curve geometry. A variety of soliton families are represented by the generalized solitonic wave profiles that are produced using the improved modified Sardar sub-equation technique, which is renowned for its accuracy and dependability. There has never been a study that used this technique before the current one. As a result, the solitonic wave structures have kink, dark, brilliant, king-singular, dark-singular, dark-bright, exponential, trigonometric, and rational solitonic structures, among other characteristics. In order to check the energy conservation, the Hamiltonian function is created and energy level demonstrated. The sensitivity analysis is also presented at various initial conditions. The graphical representation is also depicted along with the appropriate parametric values.