  Surface water waves in ideal fluids have been typically modeled by asymptotic
approximations of the full Euler equations. Some of these simplified models
lose relevant properties of the full water wave problem. One of them is the
Galilean symmetry, which is not present in important models such as the BBM
equation and the Peregrine (Classical Boussinesq) system. In this paper we
propose a mechanism to modify the above mentioned classical models and derive
new, Galilean invariant models. We present some properties of the new
equations, with special emphasis on the computation and interaction of their
solitary-wave solutions. The comparison with full Euler solutions shows the
relevance of the preservation of Galilean invariance for the description of
water waves.
