Composite electric S-brane solutions with maximal number of branes

In this paper we consider (n + 1)-dimensional cosmological model with scalar field and antisymmetric (p + 2)-form. Using an electric composite Sp-brane ansatz the field equations for the original system reduce to the equations for a Toda-like system with n(n−1)/2 quadratic constraints on the charge densities. For certain odd dimensions (D = 4m + 1 = 5, 9, 13, ...) and (p + 2)-forms (p = 2m − 1 = 1, 3, 5, ...) these algebraic constraints can be satisfied with the maximal number of charged branes (i.e. all the branes have non-zero charge densities). These solutions are characterized by self-dual or anti-self-dual charge density forms Q (of rank 2m). For these algebraic solutions with the particular D, p, Q and non-exceptional dilatonic coupling constant λ we obtain general cosmological solutions to the field equations and some properties of these solutions are highlighted (e.g. Kasner-like behavior, the existence of attractor solutions). We prove the absence of maximal configurations for p = 1 and even D (e.g. for D = 10 supergravity models and those of superstring origin).