Potential symmetries of the nonlinear wave equationutt= (uux)xand related exact and approximate solutions

This paper explores potential symmetries of the nonlinear wave equation u tt = ( uu x ) x , as well as related new similarity reductions and exact solutions of this equation. New approximate solutions of the perturbed nonlinear equations stemming from the exact solutions of the equation are obtained by applying a new approach to the use of the Lie group technique for differential equations dependent on a small parameter. In addition, some nonlinear wave equations exactly reducible to the equation u tt = ( uu x ) x are constructed using this approach.