  We investigate the case of two interacting fluids in homogeneous and
isotropic cosmologies with a non-linear interaction term. The interaction term
avoids the unrealistic form generally used in the literature, beginning with
Tolman, in which the interaction is zero when the Hubble parameter vanishes. A
variety of exact solutions for the scale factor are found and describe a range
of new behaviors. We also extend the analysis of possible cosmological
solutions with interacting fluids when curvature is taken into consideration.
We use an example of energy exchange between radiation and scalar field to
alleviate the flatness problem.
