  In Randall-Sundrum type braneworld cosmologies, the dynamical equations on
the three-brane differ from the general relativity equations by terms that
carry the effects of embedding and of the free gravitational field in the
five-dimensional bulk. In a FRW ansatze for the metric, we present two methods
for deriving inflationary solutions to the covariant non-linear dynamical
equations for the gravitational and matter fields on the brane. In the first
approach we examine the constraints on the dynamical relationship between the
cosmological scale factor and the scalar field driving self-interaction
potential, imposed by the weak energy condition. We then investigate
inflationary solutions obtained from a scalar field superpotential. Both these
techniques for solving the braneworld field equations are illustrated by flat
curvature models.
