Group Classification, Symmetry Reductions and Exact Solutions of a Generalized Korteweg-de Vries-Burgers Equation

Authors

Abdullahi Rashid Adem, International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaFollow
Chaudry Masood Khalique, International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaFollow
Motlatsi Molati, International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa\\ Department of Mathematics and Computer Science, National University of Lesotho, P.O. Roma 180, LesothoFollow

Author Country (or Countries)

South Africa

Abstract

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)

http://dx.doi.org/10.12785/amis/090158

Recommended Citation

Rashid Adem, Abdullahi; Masood Khalique, Chaudry; and Molati, Motlatsi (2015) "Group Classification, Symmetry Reductions and Exact Solutions of a Generalized Korteweg-de Vries-Burgers Equation," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 65.
DOI: http://dx.doi.org/10.12785/amis/090158
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/65