Distinct solitary wave solutions for the (۳+۱)-dimensional integrable pKP–BKP equation using the modified extended direct algebraic technique

This study aims to derive solitons and other traveling wave solutions for the pKP-BKP equation, which integrates the potential Kadomtsev–Petviashvili (pKP) and B-type Kadomtsev–Petviashvili (BKP) equations in three spatial dimensions. This equation is used to describe long water waves in oceans, impoundments, and estuaries, as well as to predict tsunamis, analyze river, tidal, and irrigation flows, and simulate weather patterns. The modified extended direct algebraic approach is employed to obtain various types of exact solutions, including dark solitons, combo dark-singular solitons, singular solitons, hyperbolic solutions, singular periodic solutions, exponential solutions, rational solutions, and Jacobi elliptic solutions. The derived solutions are visualized using Mathematica software, with contour, ۲D, and ۳D graphical representations to illustrate their dynamic behavior.

کلیدواژه ها:

pKP–BKP equation ، Dark soliton ، Rational solution ، Modified extended direct algebraic method