Exploring soliton solutions and dynamical interaction wave-form patterns of (3 + 1)-dimensional combined pKP–BKP equation

Purpose The purpose of this study is to investigate soliton solutions and dynamical interaction wave patterns of (3 + 1)-dimensional combined potential Kadomtsev–Petviashvili (pKP) using B-type Kadomtsev–Petviashvili (BKP) equation with the help of Hirota bilinear method. Design/methodology/approach Hirota bilinear method and Khater method are used to (3 + 1)-dimensional combined pKP–BKP equation for establishing the multifold solutions, containing solitons, interactions of lump, kink and periodic solutions with varying amplitudes. Findings The analytic solutions for considered model are constructed involving exponential, trigonometric, hyperbolic and quadratic functions. In addition, exact traveling wave solutions to the equation are obtained by applying modified Khater method. The dynamical characteristics of obtained solutions have been analyzed by displaying three-dimensional (3D), two-dimensional (2D) and contour profiles by considering the suitable values of involved free parameters. Hence, it illustrated the power of graphical simulations to visually convey how these solutions manifest and interact in practical scenarios. Originality/value Lump solutions, breathers, multi solitons and interaction solutions are very well furnished in this study and the physical nature of many intriguing exact solutions are illustrated using 2D, 3D and density graphs. The extracted solutions are completely new and have not been covered in other works of literature previously.