Exploration of soliton solutions of the nonlinear Kraenkel-Manna-Merle system using innovative methods in...

In this paper, the fascinating realm of the nonlinear coupled Kraenkel-Manna-Merle system is investigated. The proposed system is an effective tool used in the propagation of ferromagnetic particles in ferrite materials to realistically represent many nonlinear dynamic mechanisms in various scientific and engineering fields. First, a suitable wave transformation is applied to convert the nonlinear partial differential equation (NLPDE) into an ordinary differential equation (ODE). The next step, the Kumar-Malik method, and the new extended hyperbolic function method (nEHFM) are used to derive exact soliton solutions of the nonlinear coupled Kraenkel-Manna-Merle system. Using the offered procedures, many new soliton solutions, including Jacobi elliptic, hyperbolic, trigonometric, exponential, bright, dark, periodic, and some other singular soliton solutions, are obtained. The novelty of the solutions obtained is significant for the proposed paper. To provide a comprehensive visualization of the soliton dynamics, some of the solutions obtained are presented visually through graphical simulations of 3D, contour, and 2D plots. The outcomes of this study are novel and haven't been investigated for the main problem before. The results show that these methods are dependable, simple to use, and effective when analyzing different nonlinear models that are encountered in mathematical sciences and engineering. All solutions obtained are checked one by one with the Maple package program.