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Symmetry 2017, 9(2), 27; doi:10.3390/sym9020027

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
Received: 27 October 2016 / Accepted: 10 February 2017 / Published: 21 February 2017
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Abstract

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. View Full-Text
Keywords: (2 + 1)-dimensional Zoomeron equation; Lie point symmetries; optimal system; exact solutions; conservation laws; multiplier method (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. (CC BY 4.0).

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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.

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