Preliminary Group Classification of nonlinear wave equation utt + ut = f(x, ux)uxx + g(x, ux)

Abstract

The paper discusses the non-linear wave equations whose coefficients are dependent on first order spatial derivatives. We construct the principal Lie algebra, the equivalence Lie al- gebra, and the extensions by one of the princi- pal Lie algebra. We further construct the op- timal system of one-dimensional subalgebras for rst three extended five-dimensional Lie alge- bras. These are finally used to determine invari- ant solutions of some examples.