Higher dimensional nonlinear model arising to the diversity of fields: Dynamics of wave structures with M-fractional derivative

Abstract

In this work, we investigates the dynamics of waves of a higher dimensional nonlinear partial differential equation known as P-type (3+1)-dimensional model. This model is employed for modeling plasma waves and instabilities in plasma physics. In the context of quantum field theory and other domains, the (3+1)-dimensional p-type model is a theoretical construct that is employed to investigate a diverse array of physical processes. In addition to magnetism and the conventional theory of particle physics, this model elucidates the specific proper ties of materials and spontaneous processes in solid-state structures. In this study, we utilize the M-fractional derivative and an appropriate wave transformation for converting the governing equation into an ordinary differential equation, thereby attaining the desired exact solutions. The generalized Arnous method, F-expansion approach, and Kumar–Malik method are employed to acquire solutions. By employing these techniques, a variety of solutions are attained, such as combined, bright, dark, bright and dark, mixed, and singular solitons. The model under investigation contains a significant number of soliton solution structures. Moreover, we represent the behaviors of the solutions in 2D and 3D graphs using the appropriate parameter values. The findings presented in this study can improve the nonlinear dynamical characteristics of a specific system and validate the efficacy of the used methodologies. Our findings provide useful insights into the intricacy of nonlinear equations, enhancing prior research on the subject through the introduction of innovative techniques and the discovery of a significant number of solutions that have wide-ranging relevance.