Perturbative solutions of the Ginzburg-Landau equation and the superconducting parameters

Using the modulus-s of the elliptic function sn(theta,s) as a parameter of nonlinearity we construct the perturbative solutions of the Ginzburg-Landau equation in the presence of spatial gradients. The resulted analytical expressions describe the temperature dependence of the superconducting parameters, except the s-->1 limit. The analytical expressions which led to the temperature dependence of the superconducting parameters as the coherence length xi(t), the superconducting charge carriers concentration n(s)(t), the penetration depth lambda(t), and the thermodynamic critical field H-c(t) are found.