RESUMEN

In this paper, we study a recently proposed Ginzburg--Landau-type model for some high-T_c superconductors with d-wave pairing symmetry. The scalar complex order parameter used in the conventional Ginzburg--Landau models for low-T_c superconductors is replaced by a multi-component complex order parameter, and the free energy functional is modified accordingly to account for the symmetry properties in the setting of the d-wave pairing. A brief introduction to the physical and mathematical background of the d-wave models is provided first. We then present some rigorous mathematical analysis and discuss the relation between the new model and the conventional Ginzburg--Landau models. Various limiting cases such as the high-$\kappa$, high-field regime are examined. Numerical methods for the approximations of the new model are also considered along with results from numerical simulations that illustrate the complex structures for isolated vortices, vortex lattices and vortex motion driven by the applied current in the context of d-wave models.