Title: Localization of scalar field on the brane-world by coupling with gravity

Abstract: In this paper, we consider a general coupling mechanism between the kinetic term and the background spacetime, in which a coupling function $F(R)$ is introduced into the kinetic term of the five-dimensional scalar field. Based on this scenario, we investigate the localization of scalar fields in three specific braneworld models: the Minkowski brane, the de Sitter brane, and the Anti-de Sitter brane. For each case, different types of the effective potentials can be achieved depending on the variation of the coupling parameter in the coupling function. The Minkowski brane can exhibit volcanic-like effective potential, P\"{o}schl-Teller-like effective potential, or infinitely deep well. Both the de Sitter brane and Anti-de Sitter brane cases can realize P\"{o}schl-Teller-like effective potential, or infinitely deep well. In addition, by setting the coupling parameters to specific values, the effective potentials of both the Minkowski brane and de Sitter brane cases can possess a positive maximum at the origin of the extra dimension. Lastly, in certain cases of the Anti-de Sitter brane, the P\"{o}schl-Teller-like effective potentials allow for the existence of scalar resonances.