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South Africa


Lie group classification is performed on the generalized Korteweg-de Vries-Burgers equation ut +d uxxx +g(u)ux −nuxx + g u= f (x), which occurs in many applications of physical phenomena. We show that the equation admits a four-dimensional equivalence Lie algebra. It is also shown that the principal Lie algebra consists of a single translation symmetry. Several possible extensions of the principal Lie algebra are computed and their associated symmetry reductions and exact solutions are obtained. Also, one-dimensional optimal system of subalgebras is obtained for the case when the principal Lie algebra is extended by two symmetries.

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