Exact homoclinic wave and soliton solutions for the 2D Ginzburg–Landau equation

New exact wave solutions including homoclinic wave, kink wave and soliton solutions for the 2D Ginzburg–Landau equation are obtained using the auxiliary function method, generalized Hirota method and the ansatz function technique under the certain constraint conditions of coefficients in equation, respectively. The result shows that there exists a kink-wave solution which tends to one and the same periodic wave solution as time tends to infinite.