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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.
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Tshidiso Masebe (2022) studied this question.
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