2013/08/25 by Israel Michael Sigal, Sigal, Israel Michael
Mathematics · Physics and Astronomy · #35Q40 #35Q46 #81V99 #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #Quantum Physics (quant-ph) #math-ph #math.MP #msc:35Q40 #msc:35Q46 #msc:81V99 #nlin.PS #quant-ph
paper · pdf · doi:10.48550/arxiv.1308.5440
30 pages, 3 figures
arxiv created 2013/08/25 · arxiv updated 2013/08/27
We address the macroscopic theory of superconductivity - the Ginzburg-Landau theory. This theory %Macroscopic theory of superconductivity is based on the celebrated Ginzburg - Landau equations. First developed to explain and predict properties of superconductors, these equations form an integral part - Abelean-Higgs component - of the standard model of particle physics and, in general, have a profound influence on physics well beyond their original designation area. %These are a pair of coupled nonlinear equations for a complex function (called order parameter or Higgs field) and a vector field (magnetic potential or gauge field). They are the simplest representatives of a large family of equations appearing in physics and mathematics. (The latest variant of these equations is the Seiberg - Witten equations.)