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We study vortices in generalized Maxwell-Higgs models, 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 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.

Vortices are localized structures that appear in two spatial dimensions. They are present in many areas of nonlinear science and were firstly investigated in the context of fluid mechanics [

In high energy physics, in particular, vortices firstly appeared in the Nielsen-Olesen work [

Vortices have also been investigated in generalized models with distinct motivations in several works; see, e.g., [

Motivated by several works that appeared with generalized dynamics, we have developed a first order formalism for these models in [

Although we are working in the

To study the subject, the work is organized in a way such that in Section

We consider the generalized action

The energy-momentum tensor

The energy density

Now, we follow the route suggested in [

In order to decouple the first order equations, we introduce the generating function

We also introduce another function,

We also highlight here that the above procedure to construct the model, described by (

Let us now illustrate our procedure with some examples. We firstly suggest an

The first example arises from the generating function

In the left panel, we display the solutions

In order to construct a model that supports the solutions in (

The potential in (

The energy density can be calculated from (

The profile of the energy density in (

Another model can be generated straightforwardly from the same choice of

Here, we consider a generalization of the previous example by considering the generating function to be

In the left panel, we display the solutions

Again, to find the functions

The potential in (

The energy density is calculated from (

The energy density of (

In this work, we have developed a procedure that allows us to construct k-vortex models that support a first order framework. As we discussed above, the method is important because the constraint that dictates the form of the potential cannot be solved in general in the presence of the squared kinetic term of the scalar field,

Nevertheless, we got inspiration from the recent works [

It is worth commenting that a similar method can be developed for the more general Lagrangian density

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

We would like to acknowledge the Brazilian agency CNPq for partial financial support. D. Bazeia appreciates the support from grant 306614/2014-6, L. Losano appreciates the support from grant 303824/2017-4, M. A. Marques appreciates the support from grant 140735/2015-1, and R. Menezes appreciates the support from grant 306826/2015-1.