The resistive state in a superconducting wire: Bifurcation from the normal state
arXiv:0712.3531 · doi:10.1007/s00205-008-0188-3
Abstract
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.
References in corpus (5)
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Cited by in corpus (12)
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- Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field
- Ginzburg-Landau vortex dynamics with pinning and strong applied currents
- Influence of the boundary conditions on the current flow pattern along a superconducting wire
- Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons
- Qualitative modifications and new dynamic phases in the phase diagram of 1D superconducting wires driven with electric currents
- Justification of the Asymptotic Coupled Mode Approximation of Out-of-Plane Gap Solitons in Maxwell Equations
- Generalised Airy Operators