Group classification, symmetry reductions and exact solutions of a generalized Korteweg-de Vries-Burgers equation

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Date
2015-01-01
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Natural Sciences Publishing
Abstract
Lie group classification is performed on the generalized Korteweg-de Vries-Burgers equationut+δuxxx+g(u)ux−νuxx+γu=f(x), which occurs in many applications of physical phenomena. We show that the equation admits a four-dimensional equivalenceLie algebra. It is also shown that the principal Lie algebra consists of a single translation symmetry. Several possibleextensions of theprincipal Lie algebra are computed and their associated symmetry reductions and exact solutions are obtained. Also, one-dimensionaloptimal system of subalgebras is obtained for the case when the principal Lie algebra is extended by two symmetries.
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Keywords
Generalized Korteweg-de Vries-Burgers equation, Group classification, Symmetry reductions, Exact solutions
Citation
Adem, A. R., Khalique, C. M., & Molati, M. (2015). Group Classification, Symmetry Reductions and Exact Solutions of a Generalized Korteweg-de Vries-Burgers Equation. Appl. Math, 9(1), 501-506
URI
http://dx.doi.org/10.12785/amis/090158
 https://repository.tml.nul.ls/handle/20.500.14155/1460
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