Symmetry reduction and one-dimensional optimal system of the Hunter-Saxton equation

This study introduces the Hunter-Saxton equation to describe one model for nematic liquid crystals. We investigate the symmetry group of the Hunter-Saxton equation by applying the classical Lie symmetry methods.  Also, by utilizing the classification of one-dimensional subalgebras of the symmetry algebra for this equation, we compute the optimal system of one-parameter subalgebras. Then by using this optimal system and differential invariants, we reduce the equation and obtain the group-invariant solutions and conservation laws for the  Hunter-Saxton equation.

کلیدواژه ها:

Hunter-Saxton equation ، Optimal system ، Group-invariant solutions ، Conservation laws