Fusion of solitons, breathers, lumps, and their interactions process in B-type KP equation in quasi one-dimensional shallow water waves

Abstract In this paper, we study distinctive solutions to the (3+1)-dimensional B-type KP (BKP) equation, including lump, kink and soliton solutions with fusion phenomena. First, Hirota bilinear (HB) form is derived via Cole-Hopf transformation and HB operator. Via bilinear form and auxiliary function with specific constraints, the results concerned with lump, periodic lumps, and their interactions with kink solitons are demonstrated. Furthermore, various kinds of fusions of high order solitons are analyzed. The results related to first and second order breathers and their interaction with kink solitons are portrayed. All results are graphically displayed in 3D plots. The results reported here are new for the considered equation and have not been published elsewhere.