Codimension-1 thick brane solutions in higher-dimensional $R^n$ gravity

Vacuum plane symmetric solutions within $\alpha R^n$ modified gravity are obtained. The solutions can be regarded as describing thick branes with codimension 1 in a higher-dimensional spacetime. The dependence of the solutions on the values of four free parameters of the system under consideration is studied numerically. It is shown that when the parameter $\alpha$ increases, the solutions tend to saturation. We also show that in all cases under consideration the spacetime is asymptotically anti-de Sitter one.