The Resistive State in a Superconducting Wire: Bifurcation from the Normal State
 Jacob Rubinstein,
 Peter Sternberg,
 Kevin Zumbrun
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We study formally and rigorously the bifurcation to steady and timeperiodic states in a model for a thin superconducting wire in the presence of an imposed current. Exploiting the PTsymmetry 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 finitedimensional dynamics.
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 Title
 The Resistive State in a Superconducting Wire: Bifurcation from the Normal State
 Journal

Archive for Rational Mechanics and Analysis
Volume 195, Issue 1 , pp 117158
 Cover Date
 20100101
 DOI
 10.1007/s0020500801883
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
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 Authors

 Jacob Rubinstein ^{(1)}
 Peter Sternberg ^{(1)}
 Kevin Zumbrun ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA