Integrable spherically symmetric p-brane models associated with Lie algebras

A classical model of gravity theory with several dilatonic scalar fields and differential forms admitting an interpretation in terms of intersecting p-branes is studied in (pseudo)-Riemannian space-time $M =R_+\times S^{d_0}\times R_t\times M_2^{d_2}...\times M_n^{d_n}$ of dimension D. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so-called pseudo-Euclidean Toda-like system. We suppose that the characteristic vectors related to the configuration of p-branes and their couplings to the dilatonic scalar fields may be interpreted as the root vectors of a Lie algebra of the types $A_r, B_r, C_r$. In this case the model is reducible to one of the open Toda chain's algebraic generalization and is completely integrable by the known methods. The corresponding general solutions are presented in explicit form. The particular exact solution describing a class of nonextremal black holes is obtained and analyzed.