The phenomenon of spiral pair synchronization by oscillating strips (Nozaki-Bekki solution) in a 2D CGLE is investigated analytically. The equations describing the interaction of the strips with one another and with spirals are derived. Analysis of the equations shows that under certain conditions the strips lead to frequency and phase locking of the spirals. In this case the spiral pair (dipol...

In the inviscid limit the generalized complex Ginzburg–Landau equation reduces to the nonlinear Schrödinger equation. This limit is proved rigorously with H 1 data in the whole space for the Cauchy problem and in the torus with periodic boundary conditions. The results are valid for nonlinearities with an arbitrary growth exponent in the defocusing case and with a subcritical or critical growth...

Properties of the complexGinzburg–Landau equationwith drift are studied focusing on the Benjamin–Feir stable regime. On a finite interval with Neumann boundary conditions the equation exhibits bistability between a spatially uniform time-periodic state and a variety of nonuniform states with complex time dependence. The origin of this behavior is identified and contrasted with the bistable beha...

We show how to stabilize the uniform oscillations of the complex Ginzburg–Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful study of the spectrum of the linearized operator.

In this paper we investigate the existence and regularity of the solutions to the complex Ginzburg-Landau equation, @ t u = Au + (a + ii))u ? (b + ii)juj 2 u, on the phase space L r;p (R n) of weighted L p functions in innnite domain R n of arbitrary spatial dimensions. The unique local strong solutions are established for subcritical , i.e., r > n p ? 1. Especially, the classical Lebesgue phas...

The discovery of confined traveling waves in convection in binary fluids [Heinrichs et al., 1987; Kolodner et al., 1987; Kolodner et al., 1988; Niemela et al., 1990; Moses et al., 1987] has been a motivation for theoretical work on localized solutions of amplitude equations [Afanasjev et al., 1996; Akhmediev et al., 1996; Deissler & Brand, 1990, 1994, 1995; Fauve & Thual, 1990; Hakim & Pomeau, ...

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We show an efficient mechanism to control optical turbulence in systems with different dispersion laws, including parabolic, sub-diffractive, hyper-diffractive or general fractional dispersion. The method is based on the modification of energy cascade through spatial scales leading turbulence: a non-Hermitian spatio-temporal periodic potential allows unidirectional coupling between modes excita...

A novel chemically modified electrode containing Prussian blue complex was achieved on the surface of glass carbon electrode by sol-gel technique. The electrochemical behavior of modified electrode was characterized by cyclic voltammetry in detail. The film electrode obtained was very stable and exhibited electrocatalytic response for oxidation of nitrite. Results showed at bare GC electrode, a...