Variable coefficient complex Ginzburg-Landau equation
Abstract
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"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.
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