New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity

We investigate solutions of a new $4D$ Einstein-Gauss-Bonnet gravity ($4D$ $EGB$). We first describe the bulk vacuum solution, then we add a massive probe scalar field, and we follow considering a self-interacting scalar field which acts as a source to support thick brane solutions in the four-dimensional $EGB$ scenario with a single extra dimension of infinite extent. We illustrate our results with some distinct brane-like configurations engendering controllable thickness. It is noteworthy that such configurations are simultaneous solutions in both versions of the modified theory of gravity, the original Glavan and Lin formulation and the regularized $4D$ $EGB$.