On the stability of travelling waves arising in nematic liquid crystals

The stability of travelling waves which occur when a nematic liquid crystal is subjected to crossed electric and magnetic fields has been studied prev iously where conditions on a control parameter q for stability to occur hav e been given. This article is concerned with the behaviour of the stable pe rturbations as time increases. For each of the three travelling wave soluti ons we can determine the long-term monotonic or oscillatory behaviour of th e perturbations using knowledge of the spectrum of the operator governing t he perturbation equation.