Toda Chains with Type Am Lie Algebra for Multidimensional Classical Cosmology with Intersecting p-Branes

We consider a D-dimensional cosmological model describing an evolution of (n+1) Einstein factor spaces in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system. We consider the case, when characteristic vectors of the model, related to p-branes configuration and their couplings to the dilatonic fields, may be interpreted as the root vectors of a Lie algebra of the type Am. The model is reduced to the open Toda chain and integrated. The exact solution is presented in the Kasner-like form.