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.
Digital Object Identifier (DOI)
Rashid Adem, Abdullahi; Masood Khalique, Chaudry; and Molati, Motlatsi
"Group Classification, Symmetry Reductions and Exact Solutions of a Generalized Korteweg-de Vries-Burgers Equation,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 58.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss1/58