2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35962Multidimensional 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.10 pages, Latex., Submit. to Phys. Lett. BGeneral Relativity and Quantum Cosmologytext