The Lie Derivative and Lie Symmetries of a Telegraph Equation

Abstract:
We construct potential (nonlocal) symmetries of a Telegraph equation $u_{xx} = au_{tt} + bu_t + cu$. Ordinarily this would be done by determining the action
of a vector field on solutions of the equation. However, we adapt an alternative method devised by B. Kent Harrison and Frank Estabrook which calculates the Lie derivative of differential forms associated with the differential equation. Exact solutions of the equation are then presented.