First Order Framework for Gauge k-Vortices

We study vortices in generalized Maxwell-Higgs models, Tea Tree Oil with the inclusion of a quadratic kinetic term with the covariant derivative of the scalar field in the Lagrangian density.We discuss the stressless condition and show that the presence of analytical solutions helps us to define the model compatible with the existence of first order equations.A method to decouple the CLEAN COFFEE LIGHT ROAST first order equations and to construct the model is then introduced and, as a bonus, we get the energy depending exclusively on a function of the fields calculated from the boundary conditions.We investigate some specific possibilities and find, in particular, a compact vortex configuration in which the energy density is all concentrated in a unit circle.