Generation of multi-form exact wave solutions and linear stability analysis in the generalized (3+1)-D P-type plasma system using a modified extended mapping technique

In this work, the wave solutions of the generalized (3+1)-dimensional P-type equation, a significant model for describing the evolution of waves in plasma physics, are investigated. The modified extended mapping method (MEMM) is applied as an effective analytical tool to get these solutions. Through the use of this method, a large variety of exact solutions is successfully derived, including Jacobi elliptic function solutions, bright and dark solitons, singular solitons, exponential forms, and singular periodic waveforms solutions. These solutions provide additional insight into the complex dynamics of the used equation. Furthermore, a linear stability analysis is performed to examine the stability of the steady-state solutions. The dispersion relation shows that the perturbation growth rate is purely imaginary for generic parameters, indicating neutral stability and the absence of modulation instability. Moreover, graphical representations of some of the solutions are given in order to disclose their physical behavior and better understand the corresponding wave phenomena.