Cuscuton kinks and branes

In this paper, we study a peculiar model for the scalar field. We add the cuscuton term in a standard model and investigate how this inclusion modifies the usual behavior of kinks We find the first order equations and calculate the energy density and the total energy of the system. Also, we investigate the linear stability of the model, which is governed by a Sturm-Liouville eigenvalue equation that can be transformed in an equation of the Shcrodinger type. The model is also investigated in the braneworld scenario, where a first order formalism is also obtained and the linear stability is investigated. Surprisingly, the solutions are independent from the cuscuton term. We also show that this modification allows for the presence of analytical results in the variables that describe the transformed Schrodinger-like equation. (C) 2019 The Author(s). Published by Elsevier B.V.