  We prove in this paper a long time existence result for a modified
Boussinesq-Peregrine equation in one dimension, describing the motion of Water
Waves in shallow water, in the case of a non flat bottom. We first give a local
existence result for the original Boussinesq Peregrine equation as derived by
Boussinesq and Peregrine in all dimensions. We then introduce a new model which
has formally the same precision as the Boussinesq-Peregrine equation, and give
a local existence result in all dimensions. We finally prove a long time
existence result in dimension 1 for this new equation, without any assumption
on the smallness of the bathymetry, which is an improvement of the long time
existence result for the Boussinesq systems in the case of flat bottom.
