Accelerating cosmologies in dilatonic einstein-gauss-bonnet gravity in the string frame

We study cosmological solutions in low-energy effective heterotic string theory, which consists of the Einstein gravity with the Gauss-Bonnet term and a dilaton. And there are non-linear self-interaction terms which looks like recently studied in context of "Galileon" cosmology. We study cosmological solutions with the self-interaction term which includes two arbitrary coupling parameter. We examine the time evolution of the solutions and the question of whether the solutions can describe accelerated expansion of our four-dimensional space in the Einstein frame. We found de-Sitter solutions in our four-dimension when these two parameter are related.