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

Abundant soliton solutions on fractional Kraenkel Manna Merle model (FKMM) via new extended of generalized exponential rational function approach (GERFA)

“…It is important to note that the aforementioned method is effective, adaptable, and strong for obtaining the solitons needed for practical uses. After applying this method to the equation, several new categories of analytical solutions for the model are offered that were not previously reported in the literature [9][10][11][12]. The findings given in this research are expected to provide a solid foundation for future system applications.…”

“…Conversely, a range of innovative methods are published by different authors to investigate the nonlinear physical problems that occur in mathematical physics with the aim of obtaining exact and distinct answers. We will now introduce some of these trails using some of these techniques: Lie symmetry technique [7], extended simple equation method [8], new auxiliary equation method [9], modified auxiliary equation method [10], generalized projective riccati equations method [10], new extended direct algebraic method [11], F 6 -model expansion method [12], Kudryashov expansion method [13], etc.…”

Dynamical perspective of bifurcation analysis and soliton solutions to (1+1)-dimensional nonlinear perturbed Schrödinger model

“…For an exact solution, take into consideration using equation (1). The corresponding NLODEs is obtained by replacing an wave transformation equation (3) with equation (1).…”

“…Lastly, use Wolfram Mathematica to solve the algebraic equation systems and get the values of the parameters. The solutions for equation (1) are obtained by substituting these values into equation (4). Accurate solutions to NLPDEs, such as the (1+1)-dimensional NLPSM, may be obtained with efficiency using the MSSEA.…”

“…In a wide range of scientific domains, such as dynamics, physics, geochemistry, fluid mechanics, geophysics, plasma physics, optical fibers, and many more, the NLPDEs are crucial in characterizing the physical behavior of actual objects and dynamical processes. In today's cutting-edge scientific period, nonlinear phenomena is one of the most exciting subjects for analysts, because of its significant role in the knowledge of the actual aspects of the systems, finding the exact or analytical solutions has been a research area of interest [1,2]. It has become increasingly vital for academics to find exact answers to challenging algebraic computations using efficient computing methods.…”