Lie group analysis of the axisymmetric flow

The non-linear equations of motion describing the incompressible axisymmetric flow in a flexible and extensible circular cylindrical tube is considered. By employing Lie theory, the full one-parameter infinitesimal transformation group leaving the equations of motion invariant is derived along with its associated Lie algebra. Subgroups of the full group are then used to obtain a reduction by one in the number of independent variable in the system. These reductions are continued until a system of ordinary differential equations is reached. A series type approximate solution of these ordinary differential equations is obtained which leads to a series type approximate solutions in R2 {0} to momentum equations.