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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 is then presented. The nature of the transitions between these phases is investigated and some theoretical problems linked to the phase diagram are discussed.
We propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing nonlinearity. We dem
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
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
In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear propertie
It was recently shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, textit{Adv. Quantum Technol.} textbf{2019} textit{2}, 1800087] that the nonlinear Schrodinger equation with a simplified dissipative perturbation of special kind features a zero-velocity sol