Symmetry and singularity properties of a system of ordinary differential equations arising in the analysis of the nonlinear telegraph equations

We investigate the symmetry and similarity properties of a system of equations arising in the analysis of the nonlinear telegraph equations. The system of two equations can be decoupled and integrated. Although one of equations is linear in one of the dependent variables, we are able to perform successfully a singularity analysis. We are able to interpret the results of the singularity analysis in terms of the possibility of the existence of a subsidiary solution.