2007/12/20 by Jacob Rubinstein, Peter Sternberg, Kevin Zumbrun
Materials Science · Mathematics · Physics and Astronomy · #Amplitude #Bifurcation #Center manifold #Eigenvalues and eigenvectors #Manifold (fluid mechanics) #Nonlinear system #Organic and Molecular Conductors Research #Period-doubling bifurcation #Quantum Mechanics and Non-Hermitian Physics #Resistive touchscreen #Stationary state #Superconductivity #Topological Materials and Phenomena #math-ph #math.MP #msc:35Q60
paper · pdf · doi:10.1007/s00205-008-0188-3
arxiv created 2007/12/20 · openalex publication_date 2008/11/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study formally and rigorously the bifurcation to steady and time-periodic states in a model for a thin superconducting wire in the presence of an imposed current. Exploiting the PT-symmetry of the equations at both the linearized and nonlinear levels, and taking advantage of the collision of real eigenvalues leading to complex spectrum, we obtain explicit asymptotic formulas for the stationary solutions, for the amplitude and period of the bifurcating periodic solutions and for the location of their zeros or "phase slip centers" as they are known in the physics literature. In so doing, we construct a center manifold for the flow and give a complete description of the associated finite-dimensional dynamics.