Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system

Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived. Furthermore, the similarity variables and symmetry reductions of this new generalized two-component Hunter-Saxton system are derived. Under these Lie symmetry reductions, some exact solutions are obtained by using the symbolic computation. Moreover, a conservation law of this system is presented by using the multiplier approach. Keywords: generalized two-component Hunter-Saxton system; Lie symmetry analysis; symmetry reductions; exact solutions; conservation law Mathematics Subject Classification: 37L20, 35C05, 35Q53