Exactly solved models of interacting dark matter and dark energy
  We introduce an effective one-fluid description of the interacting dark
sector in a spatially flat Friedmann-Robertson-Walker space-time and
investigate the stability of the power-law solutions. We find the "source
equation" for the total energy density and determine the energy density of each
dark component. We study linear and nonlinear interactions which depend on the
dark matter and dark energy densities, their first derivatives, the total
energy density with its derivatives up to second order and the scale factor. We
solve the evolution equations of the dark components for both interactions,
examine exhaustively several examples and show cases where the problem of the
coincidence is alleviated. We show that a generic nonlinear interaction gives
rise to the "relaxed Chaplygin gas model" whose effective equation of state
includes the variable modified Chaplygin gas model while some others nonlinear
interactions yield de Sitter and power-law scenarios.
