Thick branes via higher order field theory models with exponential and power-law tails

In this work, we obtain exact thick brane models in 4 + 1 dimensions generated by higher order field theory kinks, inspired by specific potentials for 010 and 018 models. We verify that the geodesic equation along the fifth dimen-sion confirms the confining effects of the scalar field on the brane for all of these models. These models provide new solutions with exponential and power-law tails which live in different topological sectors. We show that the resulting branes of specific exponential law models do not possess Z2-symmetry. Furthermore, we examine the stability of the thick branes, by determining the sign of the w2 term in the expansion of the potential for the resulting Schr & ouml;dinger-like equation. It turns out that two of the three models of the 010 brane are stable, while another contains unstable modes for certain ranges of the model parameters. We also show that the brane solution from the specific 018 models are stable, while the others involve neutral equilibrium. The asymptotic behaviour of the brane solutions are also discussed.