On the Existence and Partial Stability of Standing Waves for a Nematic Liquid Crystal Director Field Equations

In this paper, following the studies in Amorim et al. (Partial Differ Equ Appl 4, 36, 2023), 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 (Commun Math Phys 85:549–561, 1982) and Hadj Selem et al. (Milan J Math 82:273–295, 2014) and we present some numerical simulations.