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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.
Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are
After a brief introduction to the complex Ginzburg-Landau equation, some of its important features in two space dimensions are reviewed. A comprehensive study of the various phases observed numerically in large systems over the whole parameter space
We study the stochastic cubic complex Ginzburg-Landau equation with complex-valued space-time white noise on the three dimensional torus. This nonlinear equation is so singular that it can only be under- stood in a renormalized sense. In the first ha
In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our prototypical example, we use the two-dimensional complex Ginzburg-Lan
We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and argume