Symmetry Analysis and Conservation Laws of the Zoomeron Equation
1
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
2
Departamento de Matemáticas, Universidad de Cádiz, P. O. Box 40, 11510 Puerto Real, Cádiz, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Roman M. Cherniha
Symmetry 2017, 9(2), 27; https://doi.org/10.3390/sym9020027
Received: 27 October 2016 / Accepted: 10 February 2017 / Published: 21 February 2017
(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models)
In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the first time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the first time, we construct the conservation laws of the underlying equation using the multiplier method.
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Keywords:
(2 + 1)-dimensional Zoomeron equation; Lie point symmetries; optimal system; exact solutions; conservation laws; multiplier method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Motsepa, T.; Khalique, C.M.; Gandarias, M.L. Symmetry Analysis and Conservation Laws of the Zoomeron Equation. Symmetry 2017, 9, 27. https://doi.org/10.3390/sym9020027
AMA Style
Motsepa T, Khalique CM, Gandarias ML. Symmetry Analysis and Conservation Laws of the Zoomeron Equation. Symmetry. 2017; 9(2):27. https://doi.org/10.3390/sym9020027
Chicago/Turabian StyleMotsepa, Tanki; Khalique, Chaudry M.; Gandarias, Maria L. 2017. "Symmetry Analysis and Conservation Laws of the Zoomeron Equation" Symmetry 9, no. 2: 27. https://doi.org/10.3390/sym9020027
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