On complex wave solutions governed by the 2D Ginzburg-Landau equation with variable coefficients

In this work, we construct new complex analytical solutions of the 2D Ginzburg-Landau equation with variable coefficients by using the unified method. We employ this method to obtain complex solitary wave solutions, complex soliton wave solutions, complex elliptic wave solutions, and complex periodic (hyperbolic) wave rational solutions. These solutions are new and may be of significant importance in nonlinear optical fibers, communication links, and soliton fiber lasers where this equation is modeled for some special physical phenomenon.