Lie symmetry analysis and conservation laws of axially uniform strings

The group invariant solution of an axially uniform string is constructed by applying the Lie symmetry method. The mathematical model of the corresponding strings is established. After introducing the infinitesimal transformations, the determining equations of Lie symmetry are proposed via Lie point transformations acting on the original equations. The infinitesimal producers of the symmetry of the system are presented with Maple. The subalgebra of the corresponding vector field pair of the system is proposed. Conserved vectors are derived through Noether's theorem. Noether conserved quantities are obtained using the structure equation satisfied by the gauge functions. In addition, the original equations of the system are converted into ordinary differential equations with the symmetry reduction method, and the explicit solutions of the reduced equations are provided.