School of Mathematics,

University of the Witwatersrand,

P Bag 3,

Wits 2050,

SOUTH AFRICA

E-mail: adavison@maths.wits.ac.za

**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.