Solitons with fission and fusion behaviors in a variable coefficient Broer–Kaup system

Using an extended homogeneous balance approach and a linear variable separation method, a general variable separation excitation of the (2 + 1)-dimensional variable coefficient Broer–Kaup (VCBK) system is derived. Based on the derived solution, we reveal soliton fission and fusion phenomena in the (2 + 1)-dimensional soliton system.