Unraveling the Bäcklund Transformation and Interaction Phenomena in Nonlinear Dispersive Media Describing Combined pKP-BKP System in (3+1) Dimensions

This work studies the exact solutions of the integrable (3+1)-dimensional combined potential Kadomtsev-Petviashvili (pKP) equation with the B-type Kadomtsev-Petviashvili (BKP) equation, which is used to characterize several nonlinear oscillations occurring in hydrodynamics, plasma physics, and nonlinear optics. A bilinear representation of the pKP-BKP model is used to study the properties of different wave solutions. A variety of ansatzes are utilized to derive lump cross-kink waves, lump cross-periodic waves, rogue waves, as well as two, three, and multi-wave solutions pertinent to the model. In addition, a traveling wave transformation is applied to transform the problem into an ordinary differential equation. The new auxiliary equation methodology yields solutions including rational, exponential, hyperbolic, and trigonometric functions. Graphical visualizations using 2D plots, contour plots, and 3D plots show the dynamics of the obtained solutions. These solutions are of great importance in nonlinear fiber optics and telecommunications, which contribute to our understanding of the fundamental physical models.