PROOF
Print ISSN: 2944-9162, E-ISSN: 2732-9941 An Open Access International Journal of Applied Science and Engineering
Volume 2, 2022
Preliminary Group Classification of nonlinear wave equation utt + ut = f(x, ux)uxx + g(x, ux)
Author: Tshidiso Masebe
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.