A generalized complex Ginzburg-Landau equation: Global existence and stability results
نویسندگان
چکیده
منابع مشابه
Bifurcation and of the Generalized Complex Ginzburg–landau Equation
We study in this paper the bifurcation and stability of the solutions of the complex Ginzburg–Landau equation(CGLE). We investigate two different modes of CGLE. We study the first mode of CGLE which has only cubic unstable nonlinear term and later we also study the second mode of CGLE which has both cubic and quintic nonlinear terms. The solutions considered in cubic CGLE bifurcate from the tri...
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Essential to the derivation of the Ginzburg-Landau equation is assumption that the spatial variables of the vector field U(x, y, t) are defined on a cylindrical domain. This means that (x, y) ∈ R ×Ω, where Ω ⊂ R is a open and bounded domain (and m ≥ 1, n ≥ 0), so that U : R ×Ω×R+ → R . The N ×N constant coefficient matrix Sμ is assumed to be non-negative, in the sense that all its eigenvalues a...
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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 ...
متن کاملNonequilibrium dynamics of the complex Ginzburg-Landau equation: analytical results.
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 ...
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We study singular patterns in a particular system of parabolic partial differential equations which consist of a GinzburgLandau equation and a mean field equation. We prove existence of the three simplest concentrated periodic stationary patterns (single spikes, double spikes, double transition layers) by composing them of more elementary patterns and solving the corresponding consistency condi...
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ژورنال
عنوان ژورنال: Communications on Pure & Applied Analysis
سال: 2021
ISSN: 1553-5258
DOI: 10.3934/cpaa.2021056