1998/07/10 by S. N. Dorogovtsev
Physics and Astronomy · Mathematics · #cond-mat #math-ph #math.MP #nlin.SI #solv-int
published as Pis'ma v ZhETF 61 (1995) 477 [JETP Lett. 61 (1995) 491] - a short version · 5 pages (epsf-LaTeX) and 3 EPS figures
arxiv created 1998/07/10 · arxiv updated 2009/11/30
An exact solution of the nonlinear nonlocal diffusion problem is obtained that describes the evolution of the magnetic flux injected into a soft or hard type-II superconductor film or a two-dimensional Josephson junction array. (The magnetic field in vortices is assumed to be perpendicular to the film; the electric field induced by the vortex motion is proportional to the local magnetic induction; flux creep in the hard superconductors under consideration is described by the logarithmic U(j) dependence.) Self-similar flux distributions with sharp square-root fronts are found. The fronts are shown to expand with power law time-dependence. A sharp peak in the middle of the distribution appears in the hard superconductor case.