  Fullerenes and nanotubes consist of a large number of carbon atoms sitting on
the sites of a regular lattice. For pratical reasons it is often useful to
approximate the equations on this lattice in terms of the continuous equation.
At the moment, the best candidate for such an equation is the modified
non-linear Schroedinger equation. In this paper, we study the modified
non-linear Schroedinger equation, which arises as continuous equation in a
system describing an excitation on a hexagonal lattice. This latter system can
e.g. describe electron-phonon interaction on fullerene related structures such
as the buckminster fullerene and nanotubes. Solutions of this modified
non-linear Schroedinger equation, which have solitonic character, can be
constructed using an Ansatz for the wave function, which has time and azimuthal
angle dependence introduced previously in the study of spinning boson stars and
Q-balls. We study these solutions on a sphere, a disc and on a cylinder.
  Our construction suggests that non-spinning as well as spinning solutions,
which have a wave function with an arbitrary number of nodes, exist. We find
that this property is closely related to the series of well-known mathematical
functions, namely the Legendre functions when studying the equation on a
sphere, the Bessel functions when studying the equation on a disc and the
trigonometric functions, respectively, when studying the equation on a
cylinder.
