  We study a modified non-linear Schroedinger equation on a 2 dimensional
sphere with radius R aiming to describe electron-phonon interactions on
fullerenes and fullerides. These electron-phonon interactions are known to be
important for the explanation of the high transition temperature of
superconducting fullerides. Like in the $R\to \infty$ limit, we are able to
construct non-spinning as well as spinning solutions which are characterised by
the number of nodes of the wave function. These solutions are closely related
to the spherical harmonic functions. For small R, we discover specific branches
of the solutions. Some of the branches survive in the $R\to\infty$ limit and
the solutions obtained on the plane ($R=\infty$) are recovered.
