Non–linear wave equations and their invariant solutions
Abstract
We carry out a preliminary group classification of the following family of non-linear
wave equations u_tt =f(u_x)u_xx+g(u_x)+x.
We first re-obtain the principal Lie algebra obtained by Ibragimov et al[3) and then
construct the equivalence Lie algebra. In order to partially classify this family of
wave equations, optimal systems of one-dimensional sub-algebras of the equivalence
Lie algebra are constructed and in so doing, two distinct equations are obtained. We
furthermore determine some invariant solutions of these equations.