Distinct solitary wave solutions for the (3+1)-dimensional integrable pKP–BKP equation using the modified extended direct algebraic technique

Authors

Nivan MohamedFollow
Hamdy Mohamed Mahmoud, Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt.Follow
Niveen Mohamed Badra, Ain Shams University
Wafaa B. Rabie, Department of Engineering Mathematics and Physics, Higher Institute of Engineering and Technology, Tanta, Egypt.Follow
Mostafa Eslami, Department of Applied Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran.Follow

Document Type

Article

Publication Date

Spring 4-29-2025

Abstract

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, 2D, and 3D graphical representations to illustrate their dynamic behavior.

Recommended Citation

10.22034/CMDE.2025.65398.3004