On the Cauchy problem for the 1+2 complex Ginzburg-Landau equation
نویسندگان
چکیده
منابع مشابه
The Complex Ginzburg-landau Equation∗
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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Several systems discussed at this workshop on Spatio-Temporal Patterns in Nonequilibrium Complex Systems have been related to or analyzed in the context of the so-called Complex Ginzburg-Landau equation (CGL). What is the difference between the physics underlying the usual amplitude description for stationary patterns and the one underlying the CGL? Why are there many more stable coherent struc...
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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.
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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 ...
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We study a complex Ginzburg-Landau equation in the plane, which has the form of a Gross-Pitaevskii equation with some dissipation added. We focus on the regime corresponding to well-prepared unitary vortices and derive their asymptotic motion law. 2000 Mathematics Subject Classification: 35B20,35B40,35Q40,82D55.
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ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1995
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s0334270000010468