Ginzburg-Landau model and its variants

In this study we consider homogeneous and inhomogeneous superconductors that can be modelled with the one-dimensional Ginzburg-Landau model and its variants, and study their behaviour under uniform applied field at temperatures below the transition temperature. Basically, we investigate the relevant models using numerical and approximate analytical methods, and observe that the results conform to physical observations.In the numerical part, we compute parameter regions where there is a unique solution, two or three different solutions depending on the reduced temperature parameter. Furthermore, we determine the stability of solutions with respect to perturbations of initial functions. In this sense, the results we obtained generalizes those reported in Kwong (1995), Chapman (1992), Aftalion (1999).Observing that equilibrium solutions requires extensive computational time, we parallelized our code and ran in a cluster of personal computers in a computer laboratory located in Faculty of Science and Letters at Karadeniz Technical University. Simulation results indicate nearly perfect performance results.On the analytical part, appropriate approximate analytical solution are obtained for several subclass of the original system. We used asymptotic, perturbation and decomposition methods to obtain approximate solutions.Finally, we analyze the relevant models with respect to the variation of one and two parameters and investigated hysteretic behavirous.