  In multi-scalar field cosmologies new dynamical degrees of freedom are
introduced which can explain the observational phenomena. Unlike the usual
scalar field theory where a single scalar field is considered, the multi-scalar
field cosmologies allow more than one scalar field and exhibits interetsing
consequences, such as quintom, hybrid inflation etc. The current work studies
the existence of exact solutions and integrable dynamical systems in
multi-scalar field cosmology. We present the exact analytic solutions for a
system of $N$-scalar fields. In particular, we consider a multi scalar field
cosmological scenario comprised of $N$-scalar fields that are minimally coupled
to the Einstein gravity. The geometry of the universe is described by the
spatially flat homogeneous and isotropic line element and the scalar fields may
interact in their kinetic or/and potential terms. Within this set up, we show
that for a specific geometry in the kinetic part of the scalar fields and
specific potential form, the gravitational field equations for the class of
$N$-scalar field models can be exactly solved. More specifically, we show that
the Einstein field equations in $N$-scalar field cosmology can be reduced to
that of a $\left( N+1\right) $ linear system.
