The Dynamics of the N-Soliton, Breather, Soliton Molecule, Lump, and Semi-Rational Solution to New (3+1)-Dimensional Combined PKP-BKP Equation

The (3 + 1)-dimensional combined pKP-BKP equation is comprehensively explored in this paper. First, N -solitons, breathers, and diverse mixed solutions made up of breathers and kink solitons are among the exact solutions of the (3 + 1)-dimensional combined pKP-BKP equation by using the Hirota bilinear method. Second, lump solutions are obtained from the long-wave limit of the N -solitons and soliton molecules are created through introducing new resonance conditions to the N -solitons. Subsequently, by offering a variety of semi-rational solutions, including lump solutions, kink solitons, and breathers, we enhance the analysis of the (3 + 1)-dimensional combined pKP-BKP equation. The dynamic behavior of these exact solutions is shown using density plots with contour lines and three-dimensional graphs.