  In this paper, following the studies of Amorim and al. in Partial Differ.Equ.
Appl. '23, we consider some new aspects of the motion of the director field of
a nematic liquid crystal submitted to a magnetic field and to a laser beam. In
particular, we study the existence and partial orbital stability of special
standing waves, in the spirit of Cazenave and Lions and Hadj Selem and al. in
Milan J. Math. '14 and we present some numerical simulations.
