Kosterlitz-Thouless vs. Ginzburg-Landau description of 2D superconducting fluctuations

We evaluate the charge and spin susceptibilities of the 2D attractive Hubbard model and we compare our results with Monte Carlo simulations on the same model. We discuss the possibility to include topological Kosterlitz-Thouless superconducting fluctuations in a standard perturbative approach substituting in the fluctuation propagator the Ginzburg-Landau correlation length with the Kosterlitz-Thouless correlation length. Received 30 June 1999     

The finite dimensional behaviour for the higher-order nonlinear Ginzburg-Landau system inn spatial dimensions

In this paper, we study the 2m-order nonlinear Ginzburg-Landau system inn spatial dimensions. We show the existence and uniqueness of the global generalized solution, and the existence of the global attractor for this system, and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractor. This project is supported by the National Natural Science Foundation of China (No. 19571010).     

Weak solutions to the two-dimensional derivative Ginzburg-Landau equation

1.IntroductionInthepreselltpaper)westudythefollowinggeneralizedcomplexGinzburg-Landauequationintwospatialdimensions:anm=pp (1 in)au~(1 lp)Ill'"~ ox,.v(lul'u) p(x,.ac)lul',(1.1)whereallparametersarereal.Thisequation3mostlyconsideredwithor=P=0anda=1,hasalongandbroadhistoryinphysicsasagenericamplitudeequationneartheonsetofinstabilitiesinfluidmechanicalsystems,aswellasinthetheoryofphasetransitionsandsuperconductivity.Inthstspecialcase,theekistenceofsolutionsandtheirlongtimebehaviourhavebeeninves…     

一维广义Ginzburg-Landau方程解的正则性及线性与非线性Galerkin近似

本文得到了一维广义Ginzburs－Landau方程解的Gevrey类正则性和关于时间的解析性．在此基础上得到线性Galerkin近似和非线性Galerkin近似的收敛性．     

The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces

In this paper, we study the limit behavior of self-similar solutions for the Complex Ginzburg-Landau (CGL) equation in the nonstandard function space E_{s,p}. We prove the uniform existence of the solutions for the CGL equation and its limit equation in E_{s,p}. Moreover we show that the self-similar solutions of CGL equation converge, globally in time, to those of its limit equation as the parameters tend to zero. Key Words Ginzburg-Landau equation; Schrödinger equation; self-similar solution; limit behavior.     

On the Global Attractor of Generalized Ginzburg-Landau Equation in One Spatial Dimension

The target of this paper is the long time behaviour of solutions for a generalized Ginzburg-Landau equation on IR. The authors establish the existence of a global attractor of finite Hausdorff and fractal dimension in a weighted Hilbert space for the equation.     

ASYMPTOTIC BEHAVIOR FOR GENERALIZED GINZBURG-LANDAU POPULATION EQUATION WITH STOCHASTIC PERTURBATION

In this paper, we are devoted to the asymptotic behavior for a nonlinear parabolic type equation of higher order with additive white noise. We focus on the Ginzburg-Landau population equation perturbed with additive noise. Firstly, we show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. And then, it is proved that under some growth conditions on the nonlinear term, this stochastic equation has a compact random attractor, which has a finite Hausdorff dimension.     

On the Zeros and Asymptotic Behavior of Minimizers to the Ginzburg-Landau Functional with Variable Coefficient

In this paper a partial answer to the fourth open problem of Bethuel-Brezis- Hélein [1] is given. When the boundary datum has topological degree ± 1, the asymptotic behavior of minimizers of the Ginzburg-Landau functional with variable coefficient \frac{1}{x_1} is given. The singular point is located.     

Exponential attractors for a generalized ginzburg-landau equation

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Exact Solutions of Discrete Complex Cubic Ginzburg-LandauEquation and Their Linear Stability

The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the G' / G-expansion method, and the linear stability of exact solutions is discussed.