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1.
91. Introduction\Nb consider thc fOllowing problemwhere Q = fl x I0, l], fl C R2 is a bounded smooth domaill, g f Z = afl x I0, l] - Sl is aC""-map such that deg(g,0O.) = d > 0 fOr all 0 5 = 5 l. Herc fl. = n x {z}. fi f Q --+ Ris a smooth function (sa}' C'(Q)) with positivc lowcr bound. ue t Q x R+ - R2.The aim of this article is to understand thc dynamics of vortices, or zeros, of solutionsu of (l.1)--(l.4). lts importance to the theory of superconductivity and applications areaddress…  相似文献
2.
Ginzburg-Landau方程动力性态的Fourier谱逼近   总被引:2,自引:0,他引:2  
0 引言和符号立方Schrodinger方程或更一般的形式Ginzburg-Landau方程出现在许多物理和化学问题中.例如在非线性光学的细束流中有方程2ikux+2⊥u+n2n0k2|u|2u=0对于二维流,有方程n2n0k2|u|2u=-2kiut-uxx-uyy还有等离子体的Langmuir波;一维单色波的自调制;二维定态平面波的自聚集;在非相对论下超导电子对在电磁场中运动等均可用非线性Schrodinger方程和Ginzburg-Landau方程来描述[1-4].另外,反应扩散方程描述的化学反应方程的研究中也出现Ginzburg-Landau方程,如相对于稳态浓度c*的扰动浓度c-c*就满足Ginzburg-Landau方程[5,6].由…  相似文献
3.
On the validity of the Ginzburg-Landau equation   总被引:1,自引:0,他引:1  
Summary The famous Ginzburg-Landau equation describes nonlinear amplitude modulations of a wave perturbation of a basic pattern when a control parameterR lies in the unstable regionO(ε 2) away from the critical valueR c for which the system loses stability. Hereε>0 is a small parameter. G-L's equation is found for a general class of nonlinear evolution problems including several classical problems from hydrodynamics and other fields of physics and chemistry. Up to now, the rigorous derivation of G-L's equation for general situations is not yet completed. This was only demonstrated for special types of solutions (steady, time periodic) or for special problems (the Swift-Hohenberg equation). Here a mathematically rigorous proof of the validity of G-L's equation is given for a general situation of one space variable and a quadratic nonlinearity. Validity is meant in the following sense. For each given initial condition in a suitable Banach space there exists a unique bounded solution of the initial value problem for G-L's equation on a finite interval of theO(1/ε2)-long time scale intrinsic to the modulation. For such a finite time interval of the intrinsic modulation time scale on which the initial value problem for G-L's equation has a bounded solution, the initial value problem for the original evolution equation with corresponding initial conditions, has a unique solutionO2) — close to the approximation induced by the solution of G-L's equation. This property guarantees that, for rather general initial conditions on the intrinsic modulation time scale, the behavior of solutions of G-L's equation is really inherited from solutions of the original problem, and the other way around: to a solution of G-L's equation corresponds a nearby exact solution with a relatively small error.  相似文献
4.
Traveling waves in the complex Ginzburg-Landau equation   总被引:1,自引:0,他引:1  
Summary In this paper we consider a modulation (or amplitude) equation that appears in the nonlinear stability analysis of reversible or nearly reversible systems. This equation is the complex Ginzburg-Landau equation with coefficients with small imaginary parts. We regard this equation as a perturbation of the real Ginzburg-Landau equation and study the persistence of the properties of the stationary solutions of the real equation under this perturbation. First we show that it is necessary to consider a two-parameter family of traveling solutions with wave speedυ and (temporal) frequencyθ; these solutions are the natural continuations of the stationary solutions of the real equation. We show that there exists a two-parameter family of traveling quasiperiodic solutions that can be regarded as a direct continuation of the two-parameter family of spatially quasi-periodic solutions of the integrable stationary real Ginzburg-Landau equation. We explicitly determine a region in the (wave speedυ, frequencyθ)-parameter space in which the weakly complex Ginzburg-Landau equation has traveling quasi-periodic solutions. There are two different one-parameter families of heteroclinic solutions in the weakly complex case. One of them consists of slowly varying plane waves; the other is directly related to the analytical solutions due to Bekki & Nozaki [3]. These solutions correspond to traveling localized structures that connect two different periodic patterns. The connections correspond to a one-parameter family of heteroclinic cycles in an o.d.e. reduction. This family of cycles is obtained by determining the limit behaviour of the traveling quasi-periodic solutions as the period of the amplitude goes to ∞. Therefore, the heteroclinic cycles merge into the stationary homoclinic solution of the real Ginzburg-Landau equation in the limit in which the imaginary terms disappear.  相似文献
5.
非自治Ginzburg-Landau方程的周期解和全局周期吸引子   总被引:1,自引:0,他引:1  
研究受周期外力影响的非自治Ginzburg-Landau方程的解的长时间行为.首先证明系统在空间H上存在周期解,而且周期解包含在空间V中的一个有界吸收集内.然后证明了当耗散系数λ满足一定条件时,该系统在空间H上具有唯一的周期解,该周期解指数吸引H中的任意有界集.  相似文献
6.
胡长流  文成林 《数学季刊》2000,15(2):102-107
本文给出一个种改进的信号多尺度估计算法,即对多尺度分解出的细节信号再继续作小波变换,对分解后得到的次平滑信号的次细节信号分别作不同程度的阈值处理,对阈值处理后的信号进行重构,作为相应尺度上的细节信号,对最粗尺度上的平滑信号进行卡尔曼滤波,再次与各尺度上细菌信号进行重构,最后得到原始尺度的信号估计值。  相似文献
7.
在假定外加磁场|h_(ex)|=o(|lnε|)以及涡旋能量以|lnε|阶爆破的前提下,借助几何测度论工具,分析了三维Ginzburg-Landau超导方程涡旋集的结构.粗略地说,它是由线段构成的一维可求长集合.  相似文献
8.
该文证明了复Ginzburg-Landau方程在非标准的函数空间Xs,p,中整体解的存在唯一性;考察了其解在X0,α+2中的极限行为,得到当参数ε→0^+或α→0,ε→0^+时,Ginzburg-Landau方程的解关于时间一致收敛到相应极限方程的解.  相似文献
9.
We study standing wave solutions in a Ginzburg-Landau equation which consists of a cubic-quintic equation stabilized by global coupling


We classify the existence and stability of all possible standing wave solutions.

  相似文献

10.
作者在三维全空间中考虑研究复Ginzburg—Landau方程(CGL)的解的长时间行为.通过引入权空间,应用内插不等式和在权空间的先验估计,获得复Ginzburg—Landau方程整体解的存在性,进一步建立了整体吸引子的存在性.  相似文献
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