Bifurcation of the London equation in anisotropic superconductors

From the superconductivity current and the general Maxwell's equations, we obtain an anisotropic London equation in terms of condensate wave function, from which the intersection, splitting and mergence of flux line are discussed. Besides the flux lines in anisotropic superconductors, our theory can also be applied to the flux lines in isotropic superconductors, the vortices in superfluids, the vortices in magnetic systems, the line defects of a two-component vector order parameter, and the wave dislocations in light beams.