International Journal of Nonlinear Analysis and Applications

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

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran

10.22075/ijnaa.2024.34657.5184

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 12 February 2025
  • Receive Date: 04 June 2024
  • Accept Date: 19 August 2024