[For the entire collection see Zbl 0742.00059.]
The authors investigate the dispersionless limit of the Kadomtsev- Petviashvili hierarchy of nonlinear evolution equations and get Benney’s moment equations. The last equations are shown to have Hamiltonian form and are proved to be integrable in the sense of Liouville. Explicit formulae for solutions of these equations with initial value data are presented in the paper. For a special case of the Lax reduction the authors consider an appropriate simplification of the equations and their solutions and in particular they construct the hodograph solutions.