Dynamics of diverse wave propagation to integrable Kraenkel–Manna–Merle system under zero damping effect in ferrites materials

In this study, we investigate the nonlinear dynamics of solitary waves in saturated ferromagnetic materials with an external field of zero conductivity. Here, we talk about how damping mechanisms affect the Kraenkel–Manna–Merle system, which controls wave propagation and expresses nonlinear ultra-short wave pulse movements in ferromagnetic materials. By using a good computational integration method called the extended Fan-sub equation technique, a number of solitary wave solutions in diverse shapes, such as hyperbolic, Jacobi’s elliptic, and trigonometric functions solutions are found. Not only do we protect periodic solutions with unknown parameters, but we also extract bell, kink, singular mixed complicated solitons. These findings demonstrate the theoretically incredibly rich soliton structures present in the system. For clarity in comprehending the solutions generated with the values of unknown parameters, two-dimensional, three-dimensional, and their contour wave profiles are plotted. The findings reveal that the integration method utilized is clear and may be extended to more complicated phenomena by using symbolic computations.