Variable coefficient complex Ginzburg-Landau equation

The complex Ginzburg-Landau equation (CGLE) is a general model of spatially extended nonequilibrium systems. In this paper, an analytical method for a variable coefficient CGLE is presented to obtain exact solutions. Variable transformations for space and time variables with coefficient functions yield an imaginary time advection equation related to a complex valued characteristic curve. The variable coefficient CGLE is transformed into the nonlinear Schr{"\o}dinger equation (NLSE) on the complex valued characteristic curve. This result indicates that the analytical solutions of the NLSE generate that of the variable coefficient CGLE.