Analytic homoclinic wave and soliton solutions for 2D coupled complex Ginzburg–Landau equations

Analytic wave solutions including homoclinic wave, kink wave and soliton solutions for the 2D coupled complex Ginzburg-Landau equations are obtained using the auxiliary function method, Hirota method and the ansatz function technique under certain constraint conditions of coefficients in equations, 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.