Cuscuton kinks and branes

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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 Shcr\"odinger type.