Nonlinear current flow around defects in superconductors

We consider nonlinear two-dimensional transport current flow J(r) in superconductors with the power-law voltage-current characteristics E proportional to J(n) and n greater than or equal to 1. We propose a general method based on a hodograph transformation which reduces this nonlinear problem to the solution of a linear London equation with the inverse screening length beta = (n - 1)/2 root n for a plate with cuts. We obtained analytical solutions for nonlinear current flow around a planar defect which causes anisotropic long-range disturbances of J(r) on the scale L similar to a root n much larger than the defect width 2a and large stagnation regions of magnetic flux near the defect. A nonanalytic crossover in J(r) was traced from the small but finite resistivity for large n to the true critical state with n --> infinity. [S003 1-9007(98)07136-1].