Elliptic function formalism description of anisotropic Ginzburg–Landau equation

Abstract

By using the elliptic function formalism, we derived exact solutions of anisotropic Ginzburg–Landau equation for materials with very large penetration depth. The solutions are described by sn( u, k) of argument u and modulus k, in the limit k→0 being approximated by sinus and in the limit k→1 we obtain the hyperbolic tangent-kink solution. The kink energy Δ E (energy gap), the topological charge S (total spin), superconducting carrier concentration n s, penetration depth λ and the critical field H c are calculated. The dependence on temperature of these parameters is achieved by the means of k. The equations of superconducting parameters are in agreement with experimental data in the temperature limit T∈(0.8 T c, T c).