In this work, we examine the prospects of matching the Kadomtsev–Petviashvili (pKP) equation with the B-type Kadomtsev–Petviashvili (BKP) equation, which we will call the pKP-BKP equation. The resulting model gives a rigorous mathematical framework for describing long wave phenomena in oceans, impoundments and estuaries and for forecasting tsunamis; river, tide and irrigation flows; and wave patterns in the atmosphere. Using a consolidated method of analysis based on symmetry reductions and rational function transformations, we obtain several classes of exact solutions composed of rational, periodic, breather and kink-wave structures. These methods shed light on the interplay between symmetries that control the formation of soliton solutions, hence allowing the construction of new families of analytical soliton solutions. The solutions obtained are linked together through spectral degeneracies and reductions in symmetry. These methodologies are presented in a systematic way, emphasizing their applicability to a general class of nonlinear evolution equations. The results of the analysis are substantiated through direct substitution, and the structural characteristics of the solutions are discussed in detail. As a result, these results expand the solution space of the pKP–BKP equation and provide better analytical insights into Kadomtsev–Petviashvili-type nonlinear evolution equations.
Raees et al. (Sat,) studied this question.