  It is known that Nambu-Goto extended objects present some pathological
structures, such as cusps and kinks, during their evolution. In this paper, we
propose a model through the generalized Raychaudhuri equation [Rh] for
membranes to determine if there are cusps and kinks in the world-sheet. We
extend the generalized Rh equation for membranes to allow the study of the
effect of higher order curvature terms in the action on the issue of cusps and
kinks, using it as a tool for determining when a Nambu-Goto string generates
cusps or kinks in its evolution. Furthermore, we present three examples where
we test graphically this approach.
