Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method

In this research work, we retrieve dynamics of new soliton solutions to the Kraenkel-Manna-Merle system which describes the nonlinear ultrashort pulse in saturated ferromagnetic materials having an external field with zero-conductivity by utilizing the new extended direct algebraic method. The soliton and other solutions achieved by this method can be categorized as a single (dark, singular), complex combo solitons as well as complex hyperbolic, plane wave and trigonometric solutions with arbitrary parameters. The spectrum of solitons is enumerated along with their existence criteria. Moreover, 2-D, 3-D, and their contour profiles of reported results are also sketched by substituting the diverse values to the parameters that facilitate the researchers to comprehend the physical phenomena of the governing equation. The results reveal the system theoretically possesses extremely rich soliton structures. The acquired solutions exhibit that the proposed technique is an efficient, valuable, and straightforward approach to constructing new solutions of various types of nonlinear partial differential equations which have important applications to applied sciences and engineering.