Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 21, No 1, (2012), 287p-298p
We consider the μCH equation which arises as an asymptotic rotator equation in a liquid crystal with a preferred direction if one takes into account the reciprocal action of dipoles on themselves. This equation is closely related to the periodic Camassa–Holm and the Hunter-Saxton equations. The μCH equation is also integrable and bi-Hamiltonian, that is, it is Hamiltonian with respect to two compatible Poisson brackets. We give a set of conjugated variables for both brackets.