  Previous work has shown that the tidal interaction between a binary system
and a circumbinary disc leads to the formation of a large inner cavity in the
disc. Subsequent formation and inward migration of a low mass planet causes it
to become trapped at the cavity edge, where it orbits until further mass growth
or disc dispersal. The question of how systems of multiple planets in
circumbinary discs evolve has not yet been addressed. Here, we present a suite
of simulations which study the evolution of pairs of planets migrating in the
disc. We also present the results of hydrodynamic simulations of five-planet
systems, and study their long term evolution after disc dispersal using a
N-body code. For the two-planet simulations we assume that the innermost planet
has migrated to the edge of the inner cavity and remains trapped there, and
study the subsequent evolution of the system as the outermost planet migrates
inward. We find that the outcomes largely depend on the mass ratio q=m_i/m_o,
where m_i (m_o) is the mass of the innermost (outermost) planet. For q<1,
planets usually undergo dynamical scattering or orbital exchange. For values of
q>1 the systems reach equilibrium configurations in which the planets are
locked into mean motion resonances, and remain trapped at the edge of the inner
cavity without further migration. Most simulations of five-planet systems we
performed resulted in collisions and scattering events, such that only a single
planet remained in orbit about the binary. In one case however, a multiplanet
resonant system was found to be dynamically stable over long time scales,
suggesting that such systems may be observed in planet searches focussed on
close binary systems.
