REDUCTIONS OF THE BENNEY EQUATIONS

The reductions of the Benney moment equations to systems of finitely m any partial differential equations are discussed. Several families of these are constructed explicitly. These must all satisfy a compatibili ty condition, and the reduced equations are diagonalisable and semi-Ha miltonian. By imposing a further constraint, of scaling and Galilean i nvariance, the compatibility condition is reduced to a system of algeb raic equations, whose solutions are described. A more general family o f reductions is then constructed explicitly.