Soliton control in temporally inhomogeneous plasmas and magneto-optical media via a variable-coefficient potential Kadomtsev–Petviashvili-B-type Kadomtsev–Petviashvili model

Temporal inhomogeneities in complex plasmas and magneto-optical media dramatically alter nonlinear wave dynamics, yet a comprehensive integrable framework accommodating all time-dependent coefficients has remained absent. We introduce a (3+1)-dimensional variable-coefficient potential Kadomtsev–Petviashvili-B-type Kadomtsev–Petviashvili (pKP-BKP) system that unifies Kadomtsev–Petviashvili (KP)-type and B-type Kadomtsev–Petviashvili (BKP)-type dynamics under temporally varying conditions. Using Painlevé analysis, we derive strict integrability-preserving constraints that reduce the six arbitrary coefficients to three physically meaningful independent functions. Additionally, we used auto-Bäcklund transformations and Hirota bilinear forms to construct N-soliton, kink, breather, singular, and lump solutions. We also observed these variable coefficients modulates amplitude, phase, velocity and width of the solitons. The solutions retain explicit dependence on the arbitrary coefficients, enabling real-time control of coherent structures. Our framework provides a unified analytical tool for nonlinear wave manipulation in inhomogeneous plasmas, magneto-optical waveguides, and ferromagnetic films, with direct applications in spintronics, optical computing, and controlled fusion environments.