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Math. Comput. Appl. 2012, 17(2), 132-139; doi:10.3390/mca17020132

Symmetry Reductions and Exact Solutions of a Variable Coefficient (2+1)-Zakharov-Kuznetsov Equation

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa
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Published: 1 August 2012
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Abstract

We study the generalized (2+1)-Zakharov-Kuznetsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. The Lie point symmetry generators of a special form of the class of equations are derived. We classify the Lie point symmetry generators to obtain the optimal system of onedimensional subalgebras of the Lie symmetry algebras. These subalgebras are then used to construct a number of symmetry reductions and exact group-invariant solutions to the underlying equation.
Keywords: Generalized ZK equation; solitons; Lie symmetries; optimal system; symmetry reduction; group-invariant solutions Generalized ZK equation; solitons; Lie symmetries; optimal system; symmetry reduction; group-invariant solutions
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Moleleki, L.D.; Johnpillai, A.G.; Khalique, C.M. Symmetry Reductions and Exact Solutions of a Variable Coefficient (2+1)-Zakharov-Kuznetsov Equation. Math. Comput. Appl. 2012, 17, 132-139.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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