论文标题
金茨堡 - 陆方方程及其概括
Ginzburg-Landau equations and their generalizations
论文作者
论文摘要
在超导理论中提出了金茨堡 - 兰道方程，以数学上描述超导体的中间状态，其中正常电导率与超导率混合在一起。后来人们理解，这些方程在数学物理学的各种问题中也起着重要作用。我们在这里提到这些方程式的扩展，以压缩Riemann表面和Riemannian 4-manifolds。一个单独的有趣的话题是涡流的散射理论，将金黄金堡 - landau方程的研究还原为研究。在这篇评论中，我们试图通过一些未解决的问题来探讨这些有趣的主题。
The Ginzburg-Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the superconductivity. It was understood later on that these equations play an important role also in various problems of mathematical physics. We mention here the extension of these equations to compact Riemann surfaces and Riemannian 4-manifolds. A separate interesting topic is the scattering theory of vortices reducing to the study of hyperbolic Ginzburg-Landau equations. In this review we tried to touch these interesting topics with some unsolved problems.
