THE ALGEBRAIC AND HAMILTONIAN-STRUCTURE OF THE DISPERSIONLESS BENNEY AND TODA HIERARCHIES

The algebraic and Hamiltonian structures of the multicomponent dispers ionless Benney and Toda hierarchies are studied. This is achieved by u sing a modified set of variables for which there is a symmetry between the basic fields. This symmetry enables formulae normally given impli citly in terms of residues, such as conserved charges and fluxes, to b e calculated explicitly. As a corollary of these results the equivalen ce of the Benney and Toda hierarchies is established. It is further sh own that such quantities may be expressed in terms of generalized hype rgeometric functions, the simplest example involving Legendre polynomi als. These results are then extended to systems derived from a rationa l Lax function and a logarithmic function. Various reductions are also studied.