In the study of telecommunication system, variable coefficient (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation is used as optical solitons transmission model, which not only explains physical meaning existing model with quintic terms, but also has more nonlinear dynamics characteristics higher dimensional system than lower system. this paper, analytical soliton solutions CGL eq...

A new voltammetric sensor for determination of uric acid (UA) by Cuppercomplex- multiwalled carbon nanotube (Cu-complex-CNT) nanocomposite modifiedcarbon paste electrode (CPE) is reported. The electrocatalytic behavior of theCu-complex-CNT nanocomposite modified CPE was studied in pH 2.0 phosphatebuffer solution by chronoamperometry (CA) and cyclic voltammetry (CV) in th...

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, meanfield theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial ...

Periodically forced oscillatory reaction–diffusion systems near the Hopf bifurcation can be modeled by the resonantly forced complex Ginzburg–Landau equation. In the 3:1 resonant locking regime this equation has three stable fixed points corresponding to the phase-locked states in the underlying reaction–diffusion system. Phase fronts separate spatial domains containing the phase-locked states....

We present a detailed analytical and numerical study of nonequilibrium dynamics for the complex Ginzburg-Landau equation. In particular, we characterize evolution morphologies using spiral defects. This paper is the first in a two-stage exposition. Here, we present analytical results for the correlation function arising from a single-spiral morphology. We also critically examine the utility of ...

We study a stochastic complex Ginzburg–Landau (CGL) equation driven by a smooth noise in space and we establish exponential convergence of the Markov transition semi-group toward a unique invariant probability measure. Since Doob Theorem does not seem not to be useful in our situation, a coupling method is used. In order to make this method easier to understand, we first focus on two simple exa...

The effect of a finite geometry on the two-dimensional complex Ginzburg-Landau equation is addressed. Boundary effects induce the formation of novel states. For example target like-solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.

Linear global modes, which are time-harmonic solutions with vanishing boundary conditions, are analysed in the context of the complex Ginzburg-Landau equation with slowly varying coefficients in doubly infinite domains. The most unstable modes are shown to be characterized by the geometry of their Stokes line network: they are found to generically correspond to a configuration with two turning ...

We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth) Calabi-Yau examples in which there are obstructions to parametrizing all of the complex structure cohomology by polynomial deformations thus requiring the analysis ba...

Reduced-order models of the nonlinear Complex Ginzburg-Landau (CGL) equation are computed using a nonlinear generalization of balanced truncation. The method involves Galerkin projection of the nonlinear dynamics onto modes determined by balanced truncation of a linearized system, and is compared to a standard method using projection onto Proper Orthogonal Decomposition (POD) modes computed fro...