  We investigate the low energy excitations of a dilute atomic Bose gas
confined in a anharmonic trap interacting with repulsive forces. The dispersion
law of both surface and compression modes are derived and analyzed for large
numbers of atoms in the trap, which show two branches of excitation and appear
a two critical value. For a upper limit, BEC can be unstable with respect to
some specific collective excitation, while for the lower limit, the frequency
of collective excitation under anharmonic influence can be effectively lower
than that without anharmonicity. Our work reveals the key role played by the
anharmonicity and interatomic forces which introduce a rich structure in the
dynamic behavior of these new many-body systems.
