Soliton Solutions, Resonance Solitons, and Some Novel Hybrid Interaction Solutions for a (3+1)-Dimensional BKP Equation in Nonlinear Optics

The central purpose of this paper is to derive novel and interesting soliton solutions for the extended (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation used in nonlinear optics and fluid mechanics. Initially, multiple soliton solutions are developed by Hirota bilinear method. Then, soliton molecule solutions, X-type soliton solutions as well as resonance Y-type soliton solutions are constructed via constraint conditions. In addition, abundant new hybrid interaction solutions are studied by assigning reasonable parameters. Finally, the stability of the considered equation is examined utilizing linear stability analysis techniques. The soliton solutions derived in this study are novel, helping us understand the nonlinear dynamics of the extended (3+1)-dimensional BKP equation.