Fission and fusion collision of high-order lumps and solitons in a (3+1)-dimensional nonlinear evolution equation

Multiple dark soliton solutions and semi-rational solutions to a (3+1)-dimensional nonlinear evolution equation are obtained by a combination of the Kadomtsev-Petviashvili hierarchy reduction method and the Hirota's bilinear method. The collision phenomena of fission and fusion of high-order lumps and solitons in the (3+1)-dimensional nonlinear evolution equation are described by these semi-rational solutions. After the collision of higher-order lumps and solitons, the lumps would fuse into or fissure from the line solitons. As lumps are created or annihilated, the exchange of energy occurs between the lumps and the line solitons.