  Multidimensional cosmological model describing the evolution of one Einstein
space of non-zero curvature and n Ricci-flat internal spaces is considered. The
action contains several dilatonic scalar fields and antisymmetric forms. When
forms are chosen to be proportional of volume forms of p-brane submanifolds of
internal space manifold, the Toda-like Lagrange representation is obtained.
Wheeler-De Witt equation for the model is presented. The exact solutions in
classical and quantum cases are obtained when dimensions of p-branes and
dilatonic couplings obey some orthogonality conditions.
