Gauge Invariant Eigenvalue Problems in

This paper is devoted to the study of the eigenvalue problems for the Ginzburg-Landau operator in the entire plane and in the half plane . The estimates for the eigenvalues are obtained and the existence of the associate eigenfunctions is proved when is a non-zero constant. These results are very useful for estimating the first eigenvalue of the Ginzburg-Landau operator with a gauge-invariant boundary condition in a bounded domain, which is closely related to estimates of the upper critical field in the theory of superconductivity.

     

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg–Landau equation instead of a Korteweg–de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.     

Attractors and Dimensions for Discretizations of a Generalized Ginzburg-Landau Equation

In this paper, we discretize the generalized Ginzburg-Landau equations with the periodic boundary condition by the finite difference method in spatial direction. It is proved that for each mesh size, there exist at tractors for the discretized systems. The bounds for the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are independtmt of tho mesh sizes.     

一维广义Ginzburg－Landau方程的指数吸引子

本文在[1]的基础上,得到了一维广义Ginzburg-Landau方程的指数吸引子的存在性。     

Soliton Solutions of Discrete Complex Ginzburg-Landau Equation via Extended Hyperbolic Function Approach

In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple,we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.     

Nonlinear Temperature Dependence of Magnetization of Two-Band Superconductors Near Upper Critical Field

Temperature dependence of the magnetization M （T） of two-band superconductors is studied in the vicinity of upper critical field He2 by using a two-band Ginzburg-Landau （GL） theory. It is shown that magnetization M（T） has a nonlinear character due to positive curvature of upper critical field Hc2（T） and temperature dependence of effective Ginzburg-Landau parameter Neff（T）. The results are shown to be in qualitative agreement with experimental data for the superconducting magnesium diboride, MgB2.     

Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps

We obtain theH ¹-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical solutions are attracted to the minimum points of the pinning functions. As a corollary, we construct a self-similar solution in the evolution of harmonic maps.     

A solution of the complex Ginzburg-Landau equation with a continuum of decay rates

We prove the existence of a uniform initial datum whose solution decays, in various Lpspaces, at different rates along different time sequences going to infinity, for complex Ginzburg-Landau equation on RN, of various parameters θ and γ.     

利用速度反馈方法控制时空混沌

以空间一维的复Ginzburg-Landau方程为模型,研究了利用系统变量随时间的变化率作为反馈控制信号控制偏微分方程系统中时空混沌的可能性.通过理论分析和数值模拟方法讨论了控制参数与可控性所满足的关系,解释了不同目标态时临界控制参数的尺寸效应. 关键词： 混沌控制 时空混沌 速度反馈 复Ginzburg-Landau方程