  We explore quintessence models of dark energy which exhibit non-minimal
coupling between the dark matter and the dark energy components of the cosmic
fluid. The kind of coupling chosen is inspired in scalar-tensor theories of
gravity. We impose a suitable dynamics of the expansion allowing to derive
exact Friedmann-Robertson-Walker solutions once the coupling function is given
as input. Self-interaction potentials of single and double exponential types
emerge as result of our choice of the coupling function. The stability and
existence of the solutions is discussed in some detail. Although, in general,
models with appropriated interaction between the components of the cosmic
mixture are useful to handle the coincidence problem, in the present study the
coincidence can not be evaded due to the choice of the solution generating
ansatz.
