Bifurcation exploration of ion acoustic solitons formation of a nonlinear beta fractional Kadomtsev-Petviashvili Burger model in plasma state

This research presents an extensive investigation of Ion acoustic soliton dynamics governed by a Beta-fractional Kadomtsev-Petviashvili-Burgurs (KPB) model. By engaging the planar dynamical system scheme in aggregation with the extended $(\phi, \psi)$ expansion, Kudryashov expansion, and the NMKM analytic schemes, we create a broad class of exact nonlinear pattern wave solutions. The local stability edifice of the fractional plasma model is explored through bifurcation theory, enabling the far-reaching classification of all admissible phase diagrams. Conforming Ion acoustic wave structures allied with every detour alignment are systematically assembled. Owing to the fractional and dissipative appearances of the model, an all-embracing assortment of soliton and nonlinear excitations containing smooth bright bell, dark bell, episodic wave, singular dark cusp wave, bright cusp wave, and kink soliton emerge as substantially germane solutions. Under electrostatic environments, the electric field and its involved field strength are scientifically extracted. The ensuing solutions seem in exponential fashion enriched by ion viscous effects, dispersion, dissipation, and weak transverse perturbations inherent to the fractional frameworks. Numerical simulations illustrate the evolution and interaction characteristics of dark bell, bright bell, and periodic surge configurations, including several revolution profiles. Both local and global stability analyses confirm the robustness of the obtained ion-acoustic results, providing deeper insight into the complex nonlinear behavior of plasma structures.