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Group Classification, Symmetry Reductions and Exact Solutions of a Generalized Korteweg-de Vries-Burgers Equation |
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PP: 501-506 |
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Author(s) |
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Abdullahi Rashid Adem,
Chaudry Masood Khalique,
Motlatsi Molati,
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Abstract |
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| 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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