Abstract
We study the thick brane model within [Formula: see text] the modified gravity in [Formula: see text]-dimensional spacetimes with [Formula: see text]. The system under consideration consists of two branes orthogonal to each other: the four-dimensional Lorentzian brane and [Formula: see text]-dimensional Euclidean one. It is numerically shown that, for a given [Formula: see text], regular vacuum asymptotically anti-de Sitter solutions exist only in the range [Formula: see text]. Depending on the values of [Formula: see text] and boundary conditions imposed on the Lorentzian brane, the solutions can pass or not pass through a fixed point located on the Lorentzian brane, and also be [Formula: see text]-symmetric or nonsymmetric. In the large-[Formula: see text] limit, we find the approximate analytic solutions. It is also shown that a test scalar field is trapped on the Lorentzian brane at any [Formula: see text].