  We consider the two scalar field cosmology in a FRW spatially flat spacetime
where the scalar fields interact both in the kinetic part and the potential. We
apply the Noether point symmetries in order to define the interaction of the
scalar fields. We use the point symmetries in order to write the field
equations in the normal coordinates and we find that the Lagrangian of the
field equations which admits at least three Noether point symmetries describes
linear Newtonian systems. Furthermore, by using the corresponding conservation
laws we find exact solutions of the field equations. Finally, we generalize our
results to the case of N scalar fields interacting both in their potential and
their kinematic part in a flat FRW background.
