  We discuss a particular stringy modular cosmology with two axion fields in
seven space-time dimensions, decomposable as a time and two flat three-spaces.
The effective equations of motion for the problem are those of the $SU(3)$ Toda
molecule, and hence are integrable. We write down the solutions, and show that
all of them are singular. They can be thought of as a generalization of the
Pre-Big-Bang cosmology with excited internal degrees of freedom, and still
suffering from the graceful exit problem. Some of the solutions however show a
rather unexpected property: some of their spatial sections shrink to a point in
spite of winding modes wrapped around them. We also comment how more general,
anisotropic, solutions, with fewer Killing symmetries can be obtained with the
help of STU dualities.
