Graviton resonances on deformed branes

Plane wave solutions of Schrodinger-like equations obtained from the metric perturbations in 5D braneworld scenarios can present resonant modes. The search for those structures is important because they can provide us massive modes with not suppressed couplings with the membrane. We propose in this paper the study of graviton Kaluza-Klein spectrum in a special kind of membrane that possesses internal structure. The interest in study of these deformed defects is because they have a more rich internal structure that has implications in the matter-energy density along the extra dimensions an this produces a space-time background whose curvature has a splitting, if compared to the usual kink-like models. Such models arise from $(4,1)$-branes constructed with one scalar field coupled with gravity where we find two-kink solutions from deformations of a $\phi^4$ potential. The main objective of this work is to observe the effects of deformation process in the resonant modes as well as in the coupling between the graviton massive modes and the brane.