Fluxbrane and S-brane solutions with polynomials related to rank-2 Lie algebras

Composite fluxbrane and S-brane solutions for a wide class of intersection rules are considered. These solutions are defined on a product manifold R_{*} x M_1 x ... x M_n which contains n Ricci-flat spaces M_1, ..., M_n with 1-dimensional factor spaces R_{*} and M_1. They are determined up to a set of functions obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. Exact solutions corresponding to configurations with two branes and intersections related to simple Lie algebras C_2 and G_2 are obtained. In these cases, the functions H_s(z), s =1,2, are polynomials of degrees (3, 4) and (6, 10), respectively, in agreement with a conjecture put forward previously in Ref., \cite{Iflux}. The S-brane solutions under consideration, for special choices of the parameters, may describe an accelerating expansion of our 3-dimensional space and a small enough variation of the effective gravitational constant.