With the help of the symbolic computation system, Maple and Riccati equation (xi ' = a(0) + a(1)xi + a(2)xi(2)), expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx + my + nt + Gamma (x, y, t) for the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system (GCBS) are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.