▁where ▁the ▁positive ▁coefficients ▁, ▁, ▁ ▁are ▁known ▁as ▁the ▁el astic ▁coefficients ▁of ▁s play , ▁tw ist , ▁and ▁b end , ▁respectively . ▁The ▁kin etic ▁energy ▁is ▁often ▁neglect ed ▁because ▁of ▁the ▁high ▁vis cos ity ▁of ▁liquid ▁cry st als . ▁ ▁Der iv ation ▁of ▁the ▁Hunter – Sa xt on ▁equation ▁▁ ▁Hunter ▁and ▁Sa xt on ▁investig ated ▁the ▁case ▁when ▁vis c ous ▁d amp ing ▁is ▁ignored ▁and ▁a ▁kin etic ▁energy ▁term ▁is ▁included ▁in ▁the ▁model . ▁Then ▁the ▁gover ning ▁equations ▁for ▁the ▁dynamics ▁of ▁the ▁director ▁field ▁are ▁the ▁E uler – L ag range ▁equations ▁for ▁the ▁L agr ang ian ▁ ▁where ▁ ▁is ▁a ▁Lag range ▁multip lier ▁corresponding ▁to ▁the ▁constraint ▁| n | = 1 . ▁They ▁restricted ▁their ▁attention ▁to ▁" s play ▁waves " ▁where ▁the ▁director ▁field ▁takes ▁the ▁special ▁form ▁ ▁This ▁assumption ▁reduces ▁the ▁L agr ang ian ▁to ▁ ▁and ▁then ▁the ▁E uler – L ag range ▁equation ▁for ▁the ▁angle ▁ φ ▁becomes ▁ ▁There ▁are ▁trivial ▁constant ▁solutions ▁ φ = φ 0 ▁corresponding ▁to ▁states ▁where ▁the ▁mole cules ▁in ▁the ▁liquid ▁cry stal ▁are ▁perfectly ▁aligned . ▁Linear ization ▁around ▁such ▁an ▁equilibrium ▁leads ▁to ▁the ▁linear ▁wave ▁equation ▁which ▁allows ▁wave ▁propag ation ▁in ▁both ▁directions ▁with ▁speed ▁, ▁so ▁the ▁non linear ▁equation ▁can ▁be ▁expected ▁to ▁behave ▁similarly . ▁In ▁order ▁to ▁study ▁right - mov ing ▁waves