On a Preliminary Group Classification Of A Quasilinear Hyperbolic Equation

Abstract

The method of preliminary group classification is applied to a general form of the quasilinear hyperbolic equation, u _tt = f (u)u _xx + g (u)² _x. As a result, we obtain an optimal system of one-dimensional subalgebras which are important to reduce the partial differential equation to an ordinary differential equation in a systematic manner. In addition, we provide the explicit forms of f(u) and g(u) for which the partial differential equation admits an additional symmetry. We also extend this classification method to potential symmetries by considering an auxiliary system where g(u) = f (u).