Multiple solitons solutions, lump solutions and rogue wave solutions of the complex cubic Ginzburg–Landau equation with the Hirota bilinear method

In this paper, we obtain the exact solutions of the (1+1) dimensional complex cubic Ginzburg–Landau equation (CCGLE) by using the Hirota bilinear method, this equation is a universal model for the evolution of the envelope of slowly varying waves packets in nonlinear dissipative media. Different types of solutions including solitons, lump and rogue wave solutions are gotten by taking different transformations. Besides, the physical significance of these solutions of CCGLE can be understood better through drawing \(\text{3D, } \text{2D }\) $\text{3D, 2D}$ and contour plots.