Breather type of chirped soliton solutions for the 2D Ginzburg–Landau equation

New exact solutions including bright soliton solutions, breather and periodic types of chirped soliton solutions, kink-wave and homoclinic wave solutions for the 2D Ginzburg–Landau equation are obtained using the special envelope transform and the auxiliary function method. It is shown that the specially envelope transform and the auxiliary function method provide a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.