Innovative Solitary Wave Solutions for the (3+1)-Dimensional Boussinesq Kadomtsev-Petviashvili-Type Equation Derived via the Improved Modified Extended Tanh-Function Method

The goal of this research is to create and analyze a novel (3+1) dimensional model that incorporates two different equations: a three-dimensional Kadomtsev-Petviashvili equation and a three-dimensional Boussinesq-KP-type equation. One of the unexpected outcomes of the idea of mixing integrable equations is a resonance of solitons. This paper presents a wide range of possible analytical solutions for the pKP–BKP equation in (3+1)-dimensions, including dark, bright, singular solitons, and other exact solutions like singular periodic, Jacobi elliptic function, rational, and exponential type. The (3+1)-dimensional B-KP-type model is subjected to the improved modified extended tanh-function approach in order to obtain novel traveling wave solutions. The employed equation plays a crucial role in describing and interpreting a broad range of non-linear phenomena seen in fluid mechanics and other nonlinear engineering and physics issues due to the strong correlation and wide range of applications of the Boussinesq-type and KP equations. The approach can help to find other kinds of solutions to the chosen equation that have not been found and published in the literature before. These solutions can aid in the comprehension of wave propagation in water wave dynamics. To further facilitate learning, they are replicated through the use of contour graphics, 2D, and 3D symbolic calculations. Moreover, linear stability analysis is discussed for the obtained solutions.