Generalization of the Kink Solution for Superconductors with Large Penetration Depths in the Ginzburg–Landau Formalism

Abstract

Exact solutions of the anisotropic Ginzburg–Landau equation are derived in the elliptic function formalism. The general class of solutions is described by sn(u|k), of argument u and modulus k, which, in the limit k<<1, is approximated by sinus and, in the limit k→1, by the well-known kink solution. The superconducting carrier concentration, ns, penetration depth, λ and critical field, Hc are calculated. The concordance with experimental data and other theories is in good agreement in the range from 0.8Tc until the critical temperature.