Investigation of the Elaborate Dynamics of Weakly Nonlinear Fractional Ion-Acoustic Waves in Magnetized Electron-Positron Plasma

This study employs three advanced computational and numerical techniques to solve the nonlinear fractional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV–ZK) equation in magnetized plasma. The reductive perturbation approach is utilized to investigate the dynamics of various components, namely isothermal species, immobile background species, and warm adiabatic fluid, in magnetized plasma. Emphasis is placed on unraveling the asymmetrical propagation characteristics of nonlinear electrostatic waves. The model’s solutions encompass diverse types of solitons, including ion-acoustic, dust acoustic, and electron acoustic solitons. Analytical solutions are obtained using a variety of mathematical functions, such as exponents, trigonometry, and hyperbolas. Two- and three-dimensional density graphs illustrate the practical behavior of a single soliton. The primary objective of employing numerical schemes is to assess the accuracy of the derived solutions, and the outcomes demonstrate the efficacy of the analytical method in solving nonlinear mathematical and physical problems. Several techniques are employed to validate the consistency between calculated and estimated results, ensuring the study’s accuracy and reliability. Overall, this investigation underscores the effectiveness of numerical and analytical techniques in tackling complex mathematical models, offering a promising avenue for future research in the field. The findings carry significant implications for comprehending nonlinear phenomena in magnetized plasma and contribute to advancing the field.